Related papers: Well-Balanced Schemes for Hyperbolic Kinetic Relax…
This paper deals with the numerical (finite volume) approximation of reaction-diffusion systems with relaxation, among which the hyperbolic extension of the Allen--Cahn equation represents a notable prototype. Appropriate discretizations…
This article proposes a highly accurate and conservative method for hyperbolic systems using the finite volume approach. This innovative scheme constructs the intermediate states at the interfaces of the control volumes using the method of…
In this paper we present a new first-order hyperbolic reformulation of the Cahn-Hilliard equation. The model is obtained from the combination of augmented Lagrangian techniques proposed earlier by the authors of this paper, with a classical…
We propose a fully discretised numerical scheme for the hyperelastic rod wave equation on the line. The convergence of the method is established. Moreover, the scheme can handle the blow-up of the derivative which naturally occurs for this…
A new approach using a hyperbolic-equation system (HES) is proposed to solve for the electron fluids in quasi-neutral plasmas. The HES approach avoids treatments of cross-diffusion terms which cause numerical instabilities in conventional…
We develop a second order well-balanced finite volume scheme for compressible Euler equations with a gravitational source term. The well-balanced property holds for arbitrary hydrostatic solutions of the corresponding Euler equations…
A series of third- and fifth-order hybrid compact least-squares central weighted essentially non-oscillatory schemes are proposed and applied to curvilinear structured grids for the finite volume method. In smooth regions, compact…
We present well-balanced, high-order, semi-discrete numerical schemes for one-dimensional blood flow models with discontinuous mechanical properties and algebraic source terms representing friction and gravity. While discontinuities in…
This work presents arbitrary high order well balanced finite volume schemes for the Euler equations with a prescribed gravitational field. It is assumed that the desired equilibrium solution is known, and we construct a scheme which is…
We introduce in this document a direct method allowing to solve numerically inverse type problems for linear hyperbolic equations. We first consider the reconstruction of the full solution of the wave equation posed in $\Omega\times (0,T)$…
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 work, the exact reproduction of a moving-water steady flow via the numerical solution of the one-dimensional shallow water equations is studied. A new scheme based on a modified version of the HLLEM approximate Riemann solver…
We address the numerical treatment of source terms in algebraic flux correction schemes for steady convection-diffusion-reaction (CDR) equations. The proposed algorithm constrains a continuous piecewise-linear finite element approximation…
We consider a one-dimensional nonlocal hyperbolic model introduced to describe the formation and movement of self-organizing collectives of animals in homogeneous 1D environments. Previous research has shown that this model exhibits a large…
We present a finite volume method that is applicable to hyperbolic PDEs including spatially varying and semilinear nonconservative systems. The spatial discretization, like that of the well-known Clawpack software, is based on solving…
We present a new multi-dimensional, robust, and cell-centered finite-volume scheme for the ideal MHD equations. This scheme relies on relaxation and splitting techniques and can be easily used at high order. A fully conservative version is…
The control of relaxation-type systems of ordinary differential equations is investigated using the Hamilton-Jacobi-Bellman equation. First, we recast the model as a singularly perturbed dynamics which we embed in a family of controlled…
This paper develops high-order well-balanced (WB) energy stable (ES) finite difference schemes for multi-layer (the number of layers $M\geqslant 2$) shallow water equations (SWEs) on both fixed and adaptive moving meshes, extending our…
In this paper, a physics-oriented stochastic kinetic scheme will be developed that includes random inputs from both flow and electromagnetic fields via a hybridization of stochastic Galerkin and collocation methods. Based on the BGK-type…
We are interested in a class of numerical schemes for the optimization of nonlinear hyperbolic partial differential equations. We present continuous and discretized relaxation schemes for scalar, one-- conservation laws. We present…