Related papers: Finite volume schemes for multilayer diffusion
A nonlinear block-coupled Finite Volume methodology is developed for large displacement and large strain regime. The new methodology uses the same normal and tangential face derivative discretisations found in the original fully coupled…
We study the convergence of the new family of mimetic finite difference schemes for linear diffusion problems recently proposed in [38]. In contrast to the conventional approach, the diffusion coefficient enters both the primary mimetic…
We present a space-time extension of a conservative Cartesian cut-cell finite-volume method for two-phase diffusion problems with prescribed interface motion. The formulation follows a two-fluid approach: one scalar field is solved in each…
We present a convergence analysis of a finite volume (FV) scheme for the multicomponent compressible Euler system in the framework of dissipative weak (DW) solutions. DW solutions were introduced as a generalized solution framework in…
The present paper introduces a class of finite volume schemes of increasing order of accuracy in space and time for hyperbolic systems that are in conservation form. This paper specifically focuses on Euler system that is used for modeling…
A finite difference numerical method is investigated for fractional order diffusion problems in one space dimension. For this, a mathematical model is developed to incorporate homogeneous Dirichlet and Neumann type boundary conditions. The…
We consider a finite volume scheme for the two-dimensional incompressible Navier-Stokes equations. We use a triangular mesh. The unknowns for the velocity and pressure are respectively piecewise constant and affine. We use a projection…
We propose and analyse a novel surface finite element method that preserves the invariant regions of systems of semilinear parabolic equations on closed compact surfaces in $\mathbb{R}^3$ under discretisation. We also provide a…
The Allen-Cahn equation is a fundamental model for phase transitions, offering critical insights into the dynamics of interface evolution in various physical systems. This paper investigates the stability and robustness of frequently…
In this article we design a finite volume semi-implicit IMEX scheme for the incompressible Navier-Stokes equations on evolving Chimera meshes. We employ a time discretization technique that separates explicit and implicit terms which…
The present work concerns the derivation of a fully well-balanced Godunov-type finite volume scheme for the Euler equations with a gravitational potential based on an approximate Riemann solver in a one-dimensional framework. It is an…
We present an implicit-explicit well-balanced finite volume scheme for the Euler equations with a gravitational source term which is able to deal also with low Mach flows. To visualize the different scales we use the non-dimensionalized…
In this paper, we study the stability of various difference approximations of the Euler-Korteweg equations. This system of evolution PDEs is a classical isentropic Euler system perturbed by a dispersive (third order) term. The Euler…
We aim at the development and analysis of the numerical schemes for approximately solving the backward diffusion-wave problem, which involves a fractional derivative in time with order $\alpha\in(1,2)$. From terminal observations at two…
Centered numerical fluxes can be constructed for compressible Euler equations which preserve kinetic energy in the semi-discrete finite volume scheme. The essential feature is that the momentum flux should be of the form $f^m_\jph =…
This paper presents a novel structure-preserving scheme for Euler equations, focusing on the numerical conservation of entropy and kinetic energy. Explicit flux functions engineered to conserve entropy are introduced within the…
This paper detailedly discusses the locally one-dimensional numerical methods for efficiently solving the three-dimensional fractional partial differential equations, including fractional advection diffusion equation and Riesz fractional…
We propose and analyze a combined finite volume--nonconforming finite element scheme on general meshes to simulate the two compressible phase flow in porous media. The diffusion term, which can be anisotropic and heterogeneous, is…
After we derive the Serre system of equations of water wave theory from a generalized variational principle, we present some of its structural properties. We also propose a robust and accurate finite volume scheme to solve these equations…
Reflected diffusions in polyhedral domains are commonly used as approximate models for stochastic processing networks in heavy traffic. Stationary distributions of such models give useful information on the steady state performance of the…