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BEGIN:VEVENT
SUMMARY:Alexander Kurgano (Southern University of Science and Technology)
DTSTART:20210823T130000Z
DTEND:20210823T135000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/1
DESCRIPTION:Title: Well-Balanced Schemes via Flux Globalization\nby Alexander
Kurgano (Southern University of Science and Technology) as part of CMO-Bou
nd-Preserving Space and Time Discretizations\n\n\nAbstract\nWe consider hy
perbolic systems of balance laws. Our goal is to develop well-balanced num
erical methods\, which respect a delicate balance between the flux and sou
rce terms and are thus capable of exactly preserving (some of the) physica
lly relevant steady-state solutions of the studied systems.\nI will introd
uce a general approach of constructing well-balanced schemes via a flux gl
obalization ap- proach: The source terms are incorporated into the fluxes.
This results in the hyperbolic system of conser- vation laws with global
fluxes. Such systems can be then integrated using Riemann-problem-solver-f
ree numerical methods. I will show several recent non-straightforward appl
ications of these well-balanced schemes.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/1/
END:VEVENT
BEGIN:VEVENT
SUMMARY:David Ketcheson (King Abdullah University of Science & Technology)
DTSTART:20210823T135000Z
DTEND:20210823T144000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/2
DESCRIPTION:Title: Time discretizations that accurately evolve a conserved or diss
ipated functional\nby David Ketcheson (King Abdullah University of Sci
ence & Technology) as part of CMO-Bound-Preserving Space and Time Discreti
zations\n\n\nAbstract\nMany mathematical models are equipped with an energ
y that is conserved or an entropy that is known to change monotonically in
time. Integrators that preserve these properties discretely are usually e
xpensive\, with the best-known examples being fully-implicit Runge-Kutta m
ethods. I will present a modification that can be applied to any integrato
r in order to preserve such a structural property. The resulting method ca
n be fully explicit\, or (depending on the functional) may require the sol
ution of a scalar algebraic equation at each step. I will present examples
to show the effectiveness of these “relaxation” methods\, and their a
dvantages over fully implicit methods or orthogonal projection. Examples w
ill include applications to compressible fluid dynamics\, dispersive nonli
near waves\, and Hamiltonian systems.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/2/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Gerardo Hernández Dueñas (Universidad Nacional Autonoma de Mexic
o)
DTSTART:20210823T151000Z
DTEND:20210823T160000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/3
DESCRIPTION:Title: Two-layer Shallow-water Flows along Channels with Arbitrary Geo
metry\nby Gerardo Hernández Dueñas (Universidad Nacional Autonoma de
Mexico) as part of CMO-Bound-Preserving Space and Time Discretizations\n\
n\nAbstract\nWe present a new high-resolution\, non-oscillatory semi-discr
ete central scheme for one-dimensional two- layer shallow-water flows alon
g channels with arbitrary cross sections and bottom topography. The scheme
extends existing central semi-discrete schemes for hyperbolic conservatio
n laws and it enjoys two properties crucial for the accurate simulation of
shallow-water flows: it preserves the positivity of the water height\, an
d it is well balanced\, i.e.\, the source terms arising from the geometry
of the channel are discretized so as to balance the non-linear hyperbolic
flux gradients. The system is integrated in time using a second order Stro
ng Stability Preserving Runge-Kutta scheme. Along with a detailed descript
ion of the scheme and proofs of these two properties\, we present several
numerical experiments that demonstrate the robustness of the numerical alg
orithm. This is joint work with Jorge Balbas.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/3/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Manuel Quezada de Luna (Universidad Nacional Autonoma de MexicoKin
g Abdullah University of Science and Technology)
DTSTART:20210823T160000Z
DTEND:20210823T165000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/4
DESCRIPTION:Title: Bound-preserving flux limiting for high-order Runge-Kutta time
discretizations of convection dominated problems\nby Manuel Quezada de
Luna (Universidad Nacional Autonoma de MexicoKing Abdullah University of
Science and Technology) as part of CMO-Bound-Preserving Space and Time Dis
cretizations\n\n\nAbstract\nWe first propose new flux limiters that have t
he structure of a flux-corrected transport (FCT) algo- rithm. These limite
rs do not depend on the time step size and\, therefore\, are applicable to
spatial semi- discretizations. Our limiters contain a user defined parame
ter that improves accuracy at a cost of a more restrictive CFL-like condit
ion\, for explicit implementations. To test the accuracy properties of the
se lim- iters\, we consider a spatial semi-discretization of Burgers’ eq
uation based on arbitrarily high-order WENO reconstructions and use the li
miters to impose global bounds.\nUsing the same WENO reconstructions\, we
obtain a full discretization based on Runge-Kutta methods. This scheme is
arbitrarily high-order and ‘essentially’ non-oscillatory but does not
preserve the maximum principle. To guarantee the maximum principle we comb
ine the fluxes of the high-order scheme with those of a low-order method b
ased on forward Euler and Local Lax-Friedrichs (LLF) fluxes. We obtain ant
i-diffusive fluxes that combine corrections in space-and-time to the low-o
rder scheme. We use our proposed limiters to guarantee the solution is max
imum principle preserving. Finally\, we present a similar methodology usin
g an arbitrarily high-order Singly Diagonal RK method combined with a low-
order scheme based on backward Euler and LLF fluxes. The implicit scheme i
s maximum principle preserving for time steps of any size.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/4/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Samuel Stechmann (King Abdullah University of Science and Technolo
gy)
DTSTART:20210823T182000Z
DTEND:20210823T191000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/5
DESCRIPTION:Title: Numerical challenges in atmospheric dynamics with moisture and
clouds\nby Samuel Stechmann (King Abdullah University of Science and T
echnology) as part of CMO-Bound-Preserving Space and Time Discretizations\
n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/5/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Martin Berzins (University of Utah)
DTSTART:20210823T191000Z
DTEND:20210823T200000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/6
DESCRIPTION:Title: Positive and/or Bounded Interpolation in time Integration - App
lications and Theory\nby Martin Berzins (University of Utah) as part o
f CMO-Bound-Preserving Space and Time Discretizations\n\n\nAbstract\nWhile
positivity and boundedness preservation plays a key role in convection do
minated problems it also plays a key in a number of situations in PDEs whe
re discrete interpolation is required. These situations include (i) Mappin
g from physics to dynamics grids in weather codes (ii) discrete remappings
in adaptive meshing (iii) particle to mesh remapping in particle in call
an material point methods (iv) solution recreation in AMR codes to address
compute node failures.\nTime integration error analysis shows how interpo
lation errors must be controlled to avoid polluting the main calculation a
nd the connection with stage errors in Runge-Kutta methods in he case of p
article methods.\nFor interpolation itself we provide a simple constructiv
e proof for an adaptive algorithm tensor-product grids on arbitrary spacin
gs to preserve boundedness and positivity and show results for cases (i) a
nd (iii) above. Reference is also made to a longer more comprehensive proo
f.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/6/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Andreas Rupp (Lappeenranta-Lahti University of Technology LUT)
DTSTART:20210824T130000Z
DTEND:20210824T135000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/7
DESCRIPTION:Title: Variations of enriched Galerkin methods for the linear advectio
n equation\nby Andreas Rupp (Lappeenranta-Lahti University of Technolo
gy LUT) as part of CMO-Bound-Preserving Space and Time Discretizations\n\n
\nAbstract\nWe interpret the enriched Galerkin (EG) method as generalizati
on of standard finite elements (contin- uous Galerkin\, CG) and of the dis
continuous Galerkin (DG) method by combining the continuous and the discon
tinuous trial spaces of CG and DG\, and by using the DG bilinear and linea
r forms.\nThen\, we introduce algebraic flux correction schemes for the st
andard enriched (P1⊕P0 and Q1⊕P0) Galerkin discretizations of the line
ar advection equation. Here\, the piecewise-constant component stabilizes
the continuous Galerkin approximation without introducing free parameters.
However\, violations of discrete maximum principles are possible in the n
eighborhood of discontinuities and steep fronts. To keep the cell averages
and the degrees of freedom of the continuous P1/Q1 component in the admis
sible range\, we limit the fluxes and element contributions\, the complete
removal of which would correspond to first-order upwinding.\nFinally\, we
discuss a further generalization of the enriched Galerkin method. The key
feature of this step is an adaptive two-mesh approach that\, in addition
to the standard enrichment of a conforming finite element discretization v
ia discontinuous degrees of freedom\, allows to subdivide selected (e.g. t
roubled) mesh cells in a non-conforming fashion and to use further discont
inuous enrichment on this finer submesh. Here\, we prove stability and sha
rp a priori error estimates for a linear advection equation under appropri
ate assumptions.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/7/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Remi Abgrall (Universität Zürich)
DTSTART:20210824T135000Z
DTEND:20210824T144000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/8
DESCRIPTION:Title: On the notion of conservation for hyperbolic problem\nby Re
mi Abgrall (Universität Zürich) as part of CMO-Bound-Preserving Space an
d Time Discretizations\n\n\nAbstract\nSince the celebrated Lax Wendroff co
nvergence theorem\, published in 1960 in CPAM\, every one knows what shoul
d be the structure of a finite volume/finite difference scheme so that one
can have a reasonable hope of convergence towards the ‘true’ entropy
solution. The proof can easily be adapted to schemes like the discontinuou
s Galerkin ones\, thought it becomes a bit less clear. There are however m
any schemes that does not fit clearly in that framework: continuous finite
element methods\, for example. Though it is relatively easy to prove a va
riant of the Lax Wendroff for them\, this does not answer the question of
the engineer: show me explicitely the flux. There are other questions rela
ted to conservation. We all know that it is forbiden by the Law to discret
ize the non conservative version of a conservative system (for example\, t
he Euler equations in primitive variables)\, and there are many counter ex
amples. However\, to which extend is that statement true? If one has an ad
ditional conservation law satisfied by the system (for example entropy con
servation for smooth solutions\, or kinetic momentum preservation)\, how c
an we modify a given ‘good’ scheme so that the modified one will satis
fy all constraints?\n\nIn this talk\, which sumarizes [1\,2\,3\,4\,5\,6]\,
I will try to show the boundaries of these statements\, and provide examp
le of schemes\, some already known\, some more recent\, that contradict\,
in some sense\, the standard beliefs. But not too much.\n\nReferences\n1.
R. Abgrall. Some remarks about conservation for residual distribution sche
mes. Computational Meth-\nods in Applied Mathematics\, 18(3):327–350\, 2
018.\n2. R. Abgrall and S. Tokareva. Staggered grid residual distribution
scheme for Lagrangian hydrodynamics.\nSIAM J. Scientific Computing\, 39(5)
:A2317–A2344\, 2017.\n3. R. Abgrall. A general framework to construct sc
hemes satisfying additional conservation relations\,\napplication to entro
py conservative and entropy dissipative schemes. J. Comput. Phys\, 372(1)\
, 2020.\n4. Nathaniel Morgan Rémi Abgrall\, Konstantin Lipnikov and Svetl
ana Tokareva. Multidimensional Stag-\ngered Grid Residual Distribution Sch
eme for Lagrangian Hydrodynamics. SIAM J. Sci. Comput.\,\n42(1):A343–A37
0\, 2020.\n5. R. Abgrall. A combination of Residual Distribution and the A
ctive Flux formulations or a new class\nof schemes that can combine severa
l writings of the same hyperbolic problem: application to the 1D\nEuler eq
uations\, 2021. https://arxiv.org/abs/2011.12572\n6. R. Abgrall\, P. Öffn
er\, and H. Ranocha. Reinterpretation and Extension of Entropy Correction
Terms\nfor Resi\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/8/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hennes Hajduk (TU Dortmund)
DTSTART:20210824T151000Z
DTEND:20210824T160000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/9
DESCRIPTION:Title: Property-preserving discontinuous Galerkin methods for solving
hyperbolic conservation laws\nby Hennes Hajduk (TU Dortmund) as part o
f CMO-Bound-Preserving Space and Time Discretizations\n\n\nAbstract\nDisco
ntinuous Galerkin (DG) methods are among the most widely used numerical di
scretization tech- niques for solving partial differential equations (PDEs
). Their local conservation property\, inherent stability\, and\, favorabl
e scalability in parallel make these schemes attractive for many applicati
ons. There are how- ever\, many shock-dominated examples\, for which even
DG methods fail to produce stable approximations. To overcome this shortco
ming\, we developed an algebraic flux limiter\, which blends a provably pr
operty- preserving low order method with a corresponding high order DG tar
get scheme. This monolithic convex limiter is primarily ]used to impose lo
cal (and global) bounds on numerical approximations\, but extensions for i
ncorporating entropy inequalities\, as well as relaxation of the constrain
ts in smooth regions are also possible. In my talk\, I will discuss the de
tails of the approach\, which include the sparsification of the low order
method\, stabilization of the numerical flux\, as well as the design of th
e monolithic limiter. Sequential limiting for products of unknowns and the
preservation of global constraints\, such as nonnegativity of pres- sure
will also be touched upon and similarities to comparable schemes will be p
ut into context. All presented numerical results were obtained with a code
that is based on the open source C++ library MFEM. The performance of the
method will be evaluated by considering a variety of classical benchmarks
for scalar conservation laws\, as well as the systems of shallow water an
d Euler equations.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/9/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Yekaterina Epshteyn (University of Utah)
DTSTART:20210824T160000Z
DTEND:20210824T165000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/10
DESCRIPTION:Title: Numerical Methods for Shallow Water Models\nby Yekaterina
Epshteyn (University of Utah) as part of CMO-Bound-Preserving Space and Ti
me Discretizations\n\n\nAbstract\nIn this talk\, we will discuss design of
structure-preserving central-upwind finite volume methods for shallow wat
er models in domains with irregular geometry and for shallow water models
with uncertainty. Shallow water models are widely used in many scientific
and engineering applications related to modeling of water flows in rivers\
, lakes and coastal areas. Shallow water equations are examples of hyperbo
lic systems of balance laws and such mathematical models can present a sig
nificant challenge for the construction of accurate and efficient numerica
l algorithms.\nWe will show that the developed structure-preserving centra
l-upwind schemes for shallow water equations deliver high-resolution\, can
handle complicated geometry\, and satisfy necessary stability conditions.
We will illustrate the performance of the designed methods on a number of
challenging numerical tests. Current and future research will be discusse
d as well.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/10/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Arturo Vargas (Lawrence Livermore National Lab)
DTSTART:20210824T182000Z
DTEND:20210824T191000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/11
DESCRIPTION:Title: GPU Accelerated ALE Remap Strategies\nby Arturo Vargas (La
wrence Livermore National Lab) as part of CMO-Bound-Preserving Space and T
ime Discretizations\n\n\nAbstract\nIn this talk we present our work in upd
ating the high-order finite element-based ALE remap method in the MARBL mu
lti-physics code from LLNL [1] for high performance on GPU platforms. MARB
L is a multi- material hydrodynamics code based on a three phase Arbitrary
-Lagrangian-Eulerian (ALE) framework: evolution of physical conservation l
aws within a moving material (Lagrangian) frame\; mesh optimization\, and
field remap. The remap step corresponds to the transfer of state variables
from the initial mesh to the optimized mesh and can often dominate the ru
n time for typical calculations. For high fidelity simulations it is imper
ative that the remap procedure be accurate\, preserve physical quantities\
, and be monotonic (not introduce new extrema). Furthermore\, for scalable
performance in large scale calculations it is imperative that the charact
eristics of the algorithm are well suited for modern computing platforms (
e.g. GPU based architectures).\nThis work is based on adopting a matrix-fr
ee algorithmic approach. The current remap algorithm in MARBL is based on
the work of Anderson and co-authors [1\, 2] which introduce a high-order a
pproach based on concepts from flux corrected transport (FCT) and a discon
tinuous Galerkin (dG) discretization for the advection equation but requir
es full matrix assembly due to its algebraic nature. Methods based on full
matrix assembly are known to have poor performance as the order of the me
thod is increased. In addition\, there are involved memory motion operatio
ns which do not work well on GPU architectures. The new matrix-free framew
ork we have been developing combines the residual distribution schemes of
Hajduk and co-authors [3\,4] with a high-order DG scheme using the clip sc
ale strategy of Anderson et al. in [5]. Lastly\, we describe the algorithm
ic tailoring for the GPU and present performance comparisons between the d
ifferent frameworks.\nThis work was performed under the auspices of the U.
S. Department of Energy by Lawrence Livermore National Laboratory under Co
ntract DE-AC52-07NA27344. LLNL-ABS-824642.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/11/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Chris Kees (LSU College of Engineering)
DTSTART:20210824T191000Z
DTEND:20210824T200000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/12
DESCRIPTION:Title: Bound-preserving discretizations for variably saturated flow i
n porous media\nby Chris Kees (LSU College of Engineering) as part of
CMO-Bound-Preserving Space and Time Discretizations\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/12/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Volker John (Weierstrass Institute for Applied Analysis and Stocha
stics)
DTSTART:20210825T130000Z
DTEND:20210825T135000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/13
DESCRIPTION:Title: Techniques for Improving Finite Element Solutions of Steady- S
tate Convection-Diffusion Equations\nby Volker John (Weierstrass Insti
tute for Applied Analysis and Stochastics) as part of CMO-Bound-Preserving
Space and Time Discretizations\n\n\nAbstract\nIn the first part of the ta
lk\, the SUPG method for continuous piecewise linear finite elements is co
nsidered. Numerical solutions computed with these methods are known to pos
sess spurious oscillations in a vicinity of layers. In [JKS11]\, a general
approach for optimizing the stabilization parameter was presented. This t
alk will address an open problem stated in this paper: the restriction of
the optimization to subregions were the choice of the stabilization parame
ter is essential. In this way\, a reduction of the dimension of the space
for optimization is achieved. Suitable algorithms are discussed and numeri
cal studies are presented. The second part of the talk deals with disconti
nuous Galerkin (DG) finite element methods. These methods are known to be
stable and to compute sharp layers in the convection-dominated regime\, bu
t also to show large spurious oscillations. Post-processing methods for re
ducing spurious oscillations are discussed\, which re- place the DG soluti
on in a vicinity of layers by a constant or linear approximation. A survey
of methods that are available in the literature is presented and several
generalizations and modifications are proposed. Numerical studies illustra
te the behavior of these methods. Details can be found in [FJ21]. This tal
k presents joint work with Ulrich Wilbrandt (WIAS) and Derk Frerichs (WIAS
).\nReferences\nFJ21 Derk Frerichs and Volker John. On reducing spurious o
scillations in dis- continuous Galerkin (DG) methods for steady-state conv
ection-diffusion equations. J. Comput. Appl. Math.\, 393:113487\, 20\, 202
1.\nJKS11 Volker John\, Petr Knobloch\, and Simona B. Savescu. A posterior
i op- timization of parameters in stabilized methods for convection-diffus
ion problems—Part I. Comput. Methods Appl. Mech. Engrg.\, 200(41-44):291
6– 2929\, 2011.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/13/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Abhinav Jha (RWTH Aachen University)
DTSTART:20210825T135000Z
DTEND:20210825T144000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/14
DESCRIPTION:Title: A Residual based a Posteriori Error Estimators for Algebraic F
lux Correction Scheme\nby Abhinav Jha (RWTH Aachen University) as part
of CMO-Bound-Preserving Space and Time Discretizations\n\n\nAbstract\nNon
-linear discretizations are necessary for convection-diffusion-reaction eq
uations for obtaining accurate solutions that satisfy the discrete maximum
principle (DMP). Algebraic stabilizations\, also known as Algebraic Flux
Correction (AFC) schemes\, belong to the very few finite element discretiz
ations that satisfy this property. Results regarding the convergence of th
e scheme [1] and efficient solution of the nonlinear system of equations [
2] have been obtained recently.. The talk is devoted to the proposal of a
new residual based a posteriori error estimator for AFC schemes. We derive
a global upper bound in the energy norm of the system which is independen
t of the choice of the limiter in the AFC scheme. We also derive a global
upper bound by combining the estimators from [3] and the AFC schemes. Nume
rical simulations in 2d are presented which support the analytical finding
s.\nReferences\n1. Gabriel R. Barrenechea\, Volker John\, and Petr Knobloc
h. Analysis of algebraic flux correction schemes. SIAM J. Numer. Anal.\, 5
4(4):2427–2451\, 2016.\n2. Abhinav Jha and Volker John. A study of solve
rs for nonlinear AFC discretizations of convection- diffusion equations. C
omput. Math. Appl.\, 78(9):3117–3138\, 2019.\n3. Volker John and Julia N
ovo. A robust SUPG norm a posteriori error estimator for stationary convec
tion- diffusion equations. Comput. Methods Appl. Mech. Engrg.\, 255:289–
305\, 2013.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/14/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Laura Saavedra Lago (Politecnica de Madrid)
DTSTART:20210825T151000Z
DTEND:20210825T160000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/15
DESCRIPTION:Title: Second order invariant domain preserving ALE approximation of
Euler equations\nby Laura Saavedra Lago (Politecnica de Madrid) as par
t of CMO-Bound-Preserving Space and Time Discretizations\n\n\nAbstract\nIn
this talk we will describe a second-order continuous finite element techn
ique for solving hyperbolic systems in the arbitrary Lagrangian Eulerian f
ramework (ALE). The main property of the method presented is that\, provid
ed the user-defined ALE velocity is reasonable\, the approximate solution
produced by the algorithm is formally second-order accurate in space\, is
conservative and preserves as many convex invariant sets of the hyperbolic
system as desired by the user\, by using a convex limiting technique. The
time stepping is explicit\, the approximation in space is done with conti
nuous finite elements.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/15/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jean-Luc Guermond (Texas A&M University)
DTSTART:20210825T160000Z
DTEND:20210825T165000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/16
DESCRIPTION:Title: Robust invariant domain preserving approximation of the compre
ssible Navier-Stokes equations\nby Jean-Luc Guermond (Texas A&M Univer
sity) as part of CMO-Bound-Preserving Space and Time Discretizations\n\n\n
Abstract\nThe objective of this talk is to present a fully-discrete approx
imation technique for the compressible Navier-Stokes equations. The method
is implicit-explicit\, second-order accurate in time and space\, and guar
anteed to be invariant domain preserving. The restriction on the time-step
size is the standard hyperbolic CFL condition. One key originality of the
method is that it is guaranteed to be conservative and invariant domain p
reserving under the standard hyperbolic CFL condition. The method is numer
ically illustrated on the OAT15a airfoil in the critical transonic regime
at Re=3 millions. This is a joint work with M. Kronbichler\, M. Maier\, B.
Popov and I. Tomas.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/16/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Eric Tovar (Texas A&M University)
DTSTART:20210825T182000Z
DTEND:20210825T191000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/17
DESCRIPTION:Title: Hyperbolic Relaxation Technique For Solving The Dispersive Ser
re Equations\nby Eric Tovar (Texas A&M University) as part of CMO-Boun
d-Preserving Space and Time Discretizations\n\n\nAbstract\nWe introduce a
relaxation technique for solving the Serre Equations for dispersive water
waves. The novelty of this technique is the reformulation of the Serre Equ
ations into a hyperbolic system which allows for explicit time stepping in
the numerical method. We then propose a second-order approximation of the
model using continuous finite elements that is well-balanced and positivi
ty preserving. The method is then numerically validated and illustrated by
comparison with laboratory experiments.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/17/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Hendrik Ranocha (University of Münster)
DTSTART:20210826T130000Z
DTEND:20210826T135000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/18
DESCRIPTION:Title: On stability of positivity-preserving Patankar-type time integ
ration methods\nby Hendrik Ranocha (University of Münster) as part of
CMO-Bound-Preserving Space and Time Discretizations\n\n\nAbstract\nPatank
ar-type scheme are linearly implicit time integration methods constructed
to satisfy positivity properties of certain ordinary differential equation
s. Since they are outside of the class of general linear methods\, they ca
n have superior positivity preserving properties. However\, standard notio
ns of stability do not apply. For example\, classical linear stability ana
lysis cannot be used since the schemes do not commute with diagonalization
. Hence\, new concepts of stability need to be introduced.\nWe provide pre
liminary investigations of stability of Patankar-type schemes. In particul
ar\, we demon- strate problematic behavior of these methods that can lead
to undesired oscillations or order reduction. Extreme cases of the latter
manifest as spurious steady states. We investigate stability properties of
vari- ous classes of Patankar-type schemes based on classical Runge-Kutta
methods\, strong stability preserving Runge-Kutta methods\, and deferred
correction schemes.\nThis project is joint work with Davide Torlo and Phil
ipp O ̈ffner.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/18/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Philipp Offner (Johannes Gutenberg University Mainz)
DTSTART:20210826T135000Z
DTEND:20210826T144000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/19
DESCRIPTION:Title: Convergence of DG Schemes for the Euler Equations via Dissipat
ive Weak Solutions\nby Philipp Offner (Johannes Gutenberg University M
ainz) as part of CMO-Bound-Preserving Space and Time Discretizations\n\n\n
Abstract\nSince the Cauchy problem for the complete Euler system is in gen
eral ill- posed in the class of admissible entropy weak solutions\, one se
arches alternatives and here the concept of dissipative weak solutions see
ms quite promising to analyze this system analytically and numerically. In
[1]\, the authors have studied the convergence properties of a class of e
ntropy dissipative finite volume schemes for the barotropic and complete c
ompressible Euler equations in the multidimensional case and could prove s
uitable stability and consistency properties to ensure convergence of the
FV schemes via dissipative measure- valued solutions. In a series of paper
\, the theory has been further developed for several (classical) FV scheme
s (of maximum order two) and have been tested numerically\, cf. [2\,3]. In
this talk\, we consider as well convergence via dissipative weak solution
s for the Euler equation\, but focus on high-order finite element based me
thods\, in particular on a specific discontinuous Galerkin schemes. For th
e convergence proof\, we need certain properties like the preservation of
several phyiscal quantities and some entropy estimates. We demonstrate how
we ensure these and prove convergence of our DG scheme via dissipative we
ak solutions. In numerical simulations\, we verify our theoretical finding
s.\nReferences\n1. E. Feireisl\, M. Luk ́aˇcov ́a-Medvid’ova ́ and H
. Mizerov ́a. Convergence of finite volume schemes for the Euler equation
s via dissipative measure-valued solutions\, Foundations of Computational
Mathematics\, 20 (4) pp. 1–44\, 2019.\n2. E. Feireisl\, M. Luk ́aˇcov
́a-Medvid’ova ́ and H. Mizerov ́a. A finite volume scheme for the Eul
er system inspired by the two velocities approach\, Numerische Mathematik\
, 144(1)\, pp. 89–132\, 2020.\n3. E. Feireisl\, M. Luk ́aˇcov ́a-Medv
id’ova ́\, B. She and Y. Wang. Computing oscillatory solutions of the E
uler system via K-convergence\, Mathematical Models and Methods in Applied
Sciences\, pp. 1–40\, 2021.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/19/
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BEGIN:VEVENT
SUMMARY:Dmitri Kuzmin (TU Dortmund University)
DTSTART:20210826T151000Z
DTEND:20210826T160000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/20
DESCRIPTION:Title: Limiter-based entropy fixes for flux-corrected discretizations
of nonlinear hyperbolic problems\nby Dmitri Kuzmin (TU Dortmund Unive
rsity) as part of CMO-Bound-Preserving Space and Time Discretizations\n\n\
nAbstract\nWe consider continuous finite element approximations of hyperbo
lic problems and modify them to satisfy relevant inequality constraints. T
he proposed approaches apply limiters to fluxes that represent the differe
nce between a high-order target scheme and a low-order property-preserving
approximation of Lax-Friedrichs type. In the first step of the limiting p
rocedure\, the given target fluxes are adjusted in a way that guarantees p
reservation of local and/or global bounds. In the second step\, additional
limiting is performed\, if necessary\, to ensure the validity of fully di
screte and/or semi-discrete entropy inequalities. The limiter-based entrop
y fixes impose entropy-conservative or entropy-dissipative bounds on entro
py production by antidiffusive fluxes and Runge-Kutta time discretizations
. We present three algorithms developed for this purpose. The semi- discre
te (SD) fix is based on Tadmor’s entropy stability theory and constrains
the spatial semi-discretization. The fully discrete explicit (FDE) fix in
corporates temporal entropy production into the flux constraints\, which m
akes them more restrictive. The fully discrete implicit (FDI) fix performs
iterative flux correction under SD-type constraints in the final Runge-Ku
tta stage. The effectiveness of these fixes is verified in numerical exper
iments for scalar equations and systems.\nReferences:\n1. D. Kuzmin and M.
Quezada de Luna\, Algebraic entropy fixes and convex limiting for continu
ous finite element discretizations of scalar hyperbolic conservation laws.
Computer Methods Appl. Mech. Engrg. 372 (2020) 113370.\n2. D. Kuzmin\, H.
Hajduk and A. Rupp\, Limiter-based entropy stabilization of semi-discrete
and fully discrete schemes for nonlinear hyperbolic problems. Preprint ar
Xiv:2107.11283 [math.NA]\, July 2021.\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/20/
END:VEVENT
BEGIN:VEVENT
SUMMARY:Jesus Bonilla (LANL)
DTSTART:20210826T160000Z
DTEND:20210826T165000Z
DTSTAMP:20260404T041458Z
UID:CMO-21w5065/21
DESCRIPTION:Title: A Positivity-Preserving Finite Element Scheme for Keller-Segel
Chemotaxis Model\nby Jesus Bonilla (LANL) as part of CMO-Bound-Preser
ving Space and Time Discretizations\n\n\nAbstract\nChemotaxis models descr
ibe the evolution of biological migration processes. In a migration proces
s\, or- ganisms (or a group of cells) migrate in response to a chemical st
imulus\, which either attracts or repels them. In this work we focus on Ke
ller-Segel equations. A model that despite its biologically inaccurate res
ults\, it is interesting and challenging from the mathematical point of vi
ew. Keller-Segel model solutions satisfy lower bounds\, and enjoy an energ
y law. The mathematical interest lies in developing numerical discretiza-
tions that yield solutions that preserve these properties\, with the aim t
o contribute and give insights into discretizations for more complex and r
ealistic chemotaxis models. Positivity-preservation is very important in t
hese models to ensure physically meaningful results and proper evolution o
f the solution. Otherwise\, it might lead to negative concentrations of ce
lls or chemo-attractant. This is especially challenging in this model beca
use\, depending on the particular initial conditions specified\, it might
lead to a blow-up of the solution. Recently\, Guti ́errez-Santacreu and R
odriguez-Galv ́an [1] have published a numerical scheme for strictly acut
e meshes\, that also yields solutions satisfying lower bounds and an energ
y law in the discrete sense. In the present work\, we aim to extend these
results to general meshes using an artificial diffusion stabilization meth
od based on [3]. Numerical results also show that the artificially added d
iffusion does not significantly smear the solution\, while it enforces low
er bounds even for solutions that blow-up in a finite time.\nReferences\n1
. J.V. Gutierr ́ez-Santacreu\, J.R. Rodriguez-Galv ́an\, Analysis of a f
ully discrete approximation for the classical Keller-Segel model: Lower an
d a priori bounds\, Comput. Math. Appl. 85 (2021) 69–81.\n2. S. Badia\,
J. Bonilla\, J.V. Gutierr ́ez-Santacreu. Solving the Keller-Segel equatio
ns with finite element approximations over general meshes\, In preparation
.\n3. Badia\, S.\, Bonilla\, J. Monotonicity-preserving finite element sch
emes based on differentiable nonlinear stabilization\, Comput. Methods App
l. Mech. Engrg. 313 (2017) 133–15\n
LOCATION:https://stable.researchseminars.org/talk/CMO-21w5065/21/
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