88 citations · 157 across the 24 of their papers we have counts for
27 papers · 1 filter
Provably fully discrete energy-stable and asymptotic-preserving scheme for barotropic Euler equations
Megala Anandan, Mária Lukáčová-Medvid'ová
We develop structure-preserving finite volume schemes for the barotropic Euler equations in the low Mach number regime. Our primary focus lies in ensuring both the asymptotic-prese…
Numerical Study of Random Kelvin-Helmholtz Instability
Alina Chertock, Michael Herty, Arsen S. Iskhakov +3
In this paper, we study random dissipative weak solutions of the compressible Euler equations in the Kelvin-Helmholtz (KH) instability. Motivated by the fact that weak entropy solu…
Structure-preserving approximation of the non-isothermal Cahn-Hilliard system based on the entropy equation
Aaron Brunk, Dennis Höhn, Mária Lukáčová-Medvidová
We propose and analyze a structure-preserving approximation of the non-isothermal Cahn-Hilliard equation using conforming finite elements for the spatial discretization and a probl…
A structure-preserving numerical method for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems
Aaron Brunk, Ansgar Jüngel, Maria Lukáčová-Medvid'ová
A conforming finite element scheme with mixed explicit-implicit time discretization for quasi-incompressible Navier-Stokes-Maxwell-Stefan systems in a bounded domain with periodic…
An asymptotic preserving scheme satisfying entropy stability for the barotropic Euler system
Megala Anandan, Mária Lukáčová-Medvid'ová, S. V. Raghurama Rao
In this paper we study structure-preserving numerical methods for low Mach number barotropic Euler equations. Besides their asymptotic preserving properties that are crucial in ord…
Solving Random Hyperbolic Conservation Laws Using Linear Programming
Shaoshuai Chu, Michael Herty, Maria Lukacova-Medvidova +1
A novel structure-preserving numerical method to solve random hyperbolic systems of conservation laws is presented. The method uses a concept of generalized, measure-valued solutio…
Convergence of a Hyperbolic Thermodynamically Compatible Finite Volume scheme for the Euler equations
Michael Dumbser, Mária Lukáčová-Medvid'ová, Andrea Thomann
We study the convergence of a novel family of thermodynamically compatible schemes for hyperbolic systems (HTC schemes) in the framework of dissipative weak solutions, applied to t…
Asymptotic preserving finite volume method for the compressible Euler equations: analysis via dissipative measure-valued solutions
K. R. Arun, Amogh Krishnamurthy, Mária Lukáčová-Medvid'ová
We propose and analyze a new asymptotic preserving (AP) finite volume scheme for the multidimensional compressible barotropic Euler equations to simulate low Mach number flows. The…
Monte Carlo method and the random isentropic Euler system
Eduard Feireisl, Mária Lukáčová-Medvid'ová, Hana Mizerová +1
We show several results on convergence of the Monte Carlo method applied to consistent approximations of the isentropic Euler system of gas dynamics with uncertain initial data. Ou…
Consistency and convergence of flux-corrected finite element methods for nonlinear hyperbolic problems
Dmitri Kuzmin, Mária Lukácova-Medvid'ová, Philipp Öffner
We investigate the consistency and convergence of flux-corrected finite element approximations in the context of nonlinear hyperbolic conservation laws. In particular, we focus on…
An implicit-explicit solver for a two-fluid single-temperature model
Mária Lukáčová-Medvid'ová, Ilya Peshkov, Andrea Thomann
We present an implicit-explicit finite volume scheme for two-fluid single-temperature flow in all Mach number regimes which is based on a symmetric hyperbolic thermodynamically com…
Convergence and error estimates of a penalization finite volume method for the compressible Navier-Stokes system
Mária Lukáčová-Medvid'ová, Bangwei She, Yuhuan Yuan
In numerical simulations a smooth domain occupied by a fluid has to be approximated by a computational domain that typically does not coincide with a physical domain. Consequently,…
On the convergence of residual distribution schemes for the compressible Euler equations via dissipative weak solutions
Rémi Abgrall, Mária Lukácova-Medvid'ová, Philipp Öffner
In this work, we prove the convergence of residual distribution schemes to dissipative weak solutions of the Euler equations. We need to guarantee that the residual distribution sc…
Local Characteristic Decomposition Based Central-Upwind Scheme
Alina Chertock, Shaoshuai Chu, Michael Herty +2
We propose novel less diffusive schemes for conservative one- and two-dimensional hyperbolic systems of nonlinear partial differential equations (PDEs). The main challenges in the…
An all Mach number finite volume method for isentropic two-phase flow
Maria Lukacova-Medvid'ova, Gabriella Puppo, Andrea Thomann
We present an implicit-explicit finite volume scheme for isentropic two phase flow in all Mach number regimes. The underlying model belongs to the class of symmetric hyperbolic the…
On a hybrid continuum-kinetic model for complex fluids
A. Chertock, P. Degond, G. Dimarco +2
In the present work, we first introduce a general framework for modelling complex multiscale fluids and then focus on the derivation and analysis of a new hybrid continuum-kinetic…
Convergence of a stochastic collocation finite volume method for the compressible Navier-Stokes system
Eduard Feireisl, Mária Lukáčová-Medvid'ová
We propose a stochastic collocation method based on the piecewise constant interpolation on the probability space combined with a finite volume method to solve the compressible Nav…
Approximating viscosity solutions of the Euler system
Eduard Feireisl, Mária Lukáčová-Medviďová, Simon Schneider +1
Applying the concept of S-convergence, based on averaging in the spirit of Strong Law of Large Numbers, the vanishing viscosity solutions of the Euler system are studied. We show h…
Asymptotic properties of a class of linearly implicit schemes for weakly compressible Euler equations
Václav Kučera, Mária Lukáčová-Medvid'ová, Sebastian Noelle +1
In this paper we derive and analyse a class of linearly implicit schemes which includes the one of Feistauer and Kučera (JCP 2007) as well as the class of RS-IMEX schemes. The impl…
Stochastic Galerkin method for cloud simulation
A. Chertock, A. Kurganov, M. Lukáčová-Medviďová +2
We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertaint…
A hybrid mass transport finite element method for Keller-Segel type systems
José Antonio Carrillo, Niklas Kolbe, Mária Lukácová-Medviďová
We propose a new splitting scheme for general reaction-taxis-diffusion systems in one spatial dimension capable to deal with simultaneous concentrated and diffusive regions as well…
Energy-stable linear schemes for polymer-solvent phase field models
Paul J. Strasser, Giordano Tierra, Burkhard Dünweg +1
We present new linear energy-stable numerical schemes for numerical simulation of complex polymer-solvent mixtures. The mathematical model proposed by Zhou, Zhang and E (Physical R…
Finite Volume Evolution Galerkin Methods for the Shallow Water Equations with Dry Beds
Andreas Bollermann, Sebastian Noelle, Maria Lukáčová - Medvidová
We present a new Finite Volume Evolution Galerkin (FVEG) scheme for the solution of the shallow water equations (SWE) with the bottom topography as a source term. Our new scheme wi…
Well-balanced finite volume evolution Galerkin methods for the shallow water equations
Maria Lukáčová - Medvidová, Sebastian Noelle, Marcus Kraft
We present a new well-balanced finite volume method within the framework of the finite volume evolution Galerkin (FVEG) schemes. The methodology will be illustrated for the shallow…