Related papers: A new thermodynamically compatible finite volume s…
Thermodynamically consistent models in continuum physics, i.e. models which satisfy the first and second laws of thermodynamics, may be expressed using the metriplectic formalism. In this work, we leverage the structures underlying this…
We introduce a novel spatio-temporal discretization for nonlinear Fokker-Planck equations on the multi-dimensional unit cube. This discretization is based on two structural properties of these equations: the first is the representation as a…
This study proposes a novel spatial discretization procedure for the compressible Euler equations which guarantees entropy conservation at a discrete level when an arbitrary equation of state is assumed. The proposed method, based on a…
A new time discretization scheme for the numerical simulation of two-phase flow governed by a thermodynamically consistent diffuse interface model is presented. The scheme is consistent in the sense that it allows for a discrete in time…
In purely non-dissipative systems, Lagrangian and Hamiltonian reduction have proven to be powerful tools for deriving physical models with exact conservation laws. We have discovered a hint that an analogous reduction method exists also for…
In this work, we develop a new hydrostatic reconstruction procedure to construct well-balanced schemes for one and multilayer shallow water flows, including wetting and drying. Initially, we derive the method for a path-conservative finite…
We are interested in the large-time behavior of solutions to finite volume discretizations of convection-diffusion equations or systems endowed with non-homogeneous Dirichlet and Neumann type boundary conditions. Our results concern various…
An energy stable finite element scheme within arbitrary Lagrangian Eulerian (ALE) framework is derived for simulating the dynamics of millimetric droplets in contact with solid surfaces. Supporting surfaces considered may exhibit…
The main purpose of the present paper is to solve the thermodynamic inconsistencies that result when deriving equivalent micropolar models of periodic beam-lattice materials through standard continualization schemes. In fact, this technique…
Developing high-order numerical schemes for two-phase flow in porous media that preserve key physical properties remains a significant challenge in numerical analysis. In this article, we propose a general framework to construct fully…
We propose a finite element discretisation approach for the incompressible Euler equations which mimics their geometric structure and their variational derivation. In particular, we derive a finite element method that arises from a…
High order schemes are known to be unstable in the presence of shock discontinuities or under-resolved solution features for nonlinear conservation laws. Entropy stable schemes address this instability by ensuring that physically relevant…
In this article we present the first better than second order accurate unstructured Lagrangian-type one-step WENO finite volume scheme for the solution of hyperbolic partial differential equations with non-conservative products. The method…
In this paper, we present a general numerical platform for designing accurate, efficient, and stable numerical algorithms for incompressible hydrodynamic models that obeys the thermodynamical laws. The obtained numerical schemes are…
We present a novel cell-centered direct Arbitrary-Lagrangian-Eulerian (ALE) finite volume scheme on unstructured triangular meshes that is high order accurate in space and time and that also allows for time-accurate local time stepping…
This work is devoted to the numerical approximation of high-dimensional advection-diffusion equations. It is well-known that classical methods, such as the finite volume method, suffer from the curse of dimensionality, and that their time…
We propose a new fractional Laplacian for bounded domains, expressed as a conservation law and thus particularly suited to finite-volume schemes. Our approach permits the direct prescription of no-flux boundary conditions. We first show the…
This paper is concerned with a rigorous convergence analysis of a fully discrete Lagrangian scheme for the Hele-Shaw flow, which is the fourth order thin-film equation with linear mobility in one space dimension. The discretization is based…
A fully discrete Galerkin scheme for a thermodynamically consistent transient Max-well-Stefan system for the mass particle densities, coupled to the Poisson equation for the electric potential, is investigated. The system models the…
Well balanced and free energy dissipative first- and second-order accurate finite volume schemes are proposed for a general class of hydrodynamic systems with linear and nonlinear damping. The natural Liapunov functional of the system,…