Related papers: Numerical Approximation of Hyperbolic Systems Cont…
The paper is concerned with the mathematical theory and numerical approximation of systems of partial differential equations (pde) of hyperbolic, pseudo-parabolic type. Some mathematical properties of the initial-boundary-value problem…
We consider a class of multiscale parabolic problems with diffusion coefficients oscillating in space at a possibly small scale $\varepsilon$. Numerical homogenization methods are popular for such problems, because they capture efficiently…
The regularisation of nonlinear hyperbolic conservation laws has been a problem of great importance for achieving uniqueness of weak solutions and also for accurate numerical simulations. In a recent work, the first two authors proposed a…
We study a first-order hyperbolic approximation of the nonlinear Schr\"odinger (NLS) equation. We show that the system is strictly hyperbolic and possesses a modified Hamiltonian structure, along with at least three conserved quantities…
The paper describes the qualitative structure of BV entropy solutions of a strictly hyperbolic system of balance laws with characteristic fields either piecewise genuinely nonlinear or linearly degenerate. In particular, we provide an…
Solutions of initial-boundary value problems for systems of conservation laws depend on the underlying viscous mechanism, namely different viscosity operators lead to different limit solutions. Standard numerical schemes for approximating…
The effectiveness of the hyperbolic relaxation method for solving the Einstein constraint equations numerically is studied here on a variety of compact orientable three-manifolds. Convergent numerical solutions are found using this method…
In this paper, we consider mathematical modeling and numerical simulation of non-isothermal compressible multi-component diffuse-interface two-phase flows with realistic equations of state. A general model with general reference velocity is…
The capability to accurately predict flood flows via numerical simulations is a key component of contemporary flood risk management practice. However, modern flood models lack the capacity to accurately model flow interactions with linear…
The proposed method aims to approximate a solution of a fluid-fluid interaction problem in case of low viscosities. The nonlinear interface condition on the joint boundary allows for this problem to be viewed as a simplified version of the…
A fully conservative sharp-interface method is developed for multiphase flows with phase change. The coupling between two phases is implemented via introducing the interfacial fluxes, which are obtained by solving a general Riemann problem…
We are concerned with fully-discrete schemes for the numerical approximation of diffusive-dispersive hyperbolic conservation laws with a discontinuous flux function in one-space dimension. More precisely, we show the convergence of…
We introduce an adaptive viscosity regularization approach for the numerical solution of systems of nonlinear conservation laws with shock waves. The approach seeks to solve a sequence of regularized problems consisting of the system of…
Entropy solutions have been widely accepted as the suitable solution framework for systems of conservation laws in several space dimensions. However, recent results in \cite{CDL1,CDL2} have demonstrated that entropy solutions may not be…
In this paper, we present an accurate numerical method for the time-harmonic Maxwell's equations for bi-periodic multilayered media with quasi-periodic incident waves using the Method of Fundamental Solutions in conjunction with a…
We use high order finite difference methods to solve the wave equation in the second order form. The spatial discretization is performed by finite difference operators satisfying a summation-by-parts property. The focus of this work is on…
This work focuses on the development of a self adjusting multirate strategy based on an implicit time discretization for the numerical solution of hyperbolic equations, that could benefit from different time steps in different areas of the…
In this paper we propose a Godunov-based discretization of a hyperbolic system of conservation laws with discontinuous flux, modeling vehicular flow on a network. Each equation describes the density evolution of vehicles having a common…
We consider a loosely coupled, non-iterative Robin-Robin coupling method proposed and analyzed in [J. Numer. Math., 31(1):59--77, 2023] for a parabolic-parabolic interface problem and prove estimates for the discrete time derivatives of the…
Numerical methods for the Euler equations with a singular source are discussed in this paper. The stationary discontinuity induced by the singular source and its coupling with the convection of fluid presents challenges to numerical…