Related papers: Variable relaxed schemes for multidimensional hype…
This paper presents the construction of two numerical schemes for the solution of hyperbolic systems with relaxation source terms. The methods are built by considering the relaxation system as a whole, without separating the resolution of…
This work concerns the numerical approximation with a finite volume method of inviscid, nonequilibrium, high-temperature flows in multiple space dimensions. It is devoted to the analysis of the numerical scheme for the approximation of the…
We investigate the time-asymptotic stability of the Jin-Xin model and its diffusive relaxation limit toward viscous conservation laws in $\mathbb{R}^d$ for $d\geq 1$. First, we establish a priori estimates that are uniform with respect to…
We extend to multi-dimensions the work of [1], where new fully explicit kinetic methods were built for the approximation of linear and non-linear convection-diffusion problems. The fundamental principles from the earlier work are retained:…
We consider a nonlinear variational wave equation that models the dynamics of the director field in nematic liquid crystals with high molecular rotational inertia. Being derived from an energy principle, energy stability is an intrinsic…
The over-relaxation approach is an alternative to the Jin-Xin relaxation method (Jin and Xin [1]) in order to apply the equilibrium source term in a more precise way (Coulette et al. [2, 3]). This is also a key ingredient of the…
In this paper, we propose a variable time-step linear relaxation scheme for time-fractional phase-field equations with a free energy density in general polynomial form. The $L1^{+}$-CN formula is used to discretize the fractional…
A general procedure to construct a class of simple and efficient high resolution Total Variation Diminishing (TVD) schemes for non-linear hyperbolic conservation laws by introducing anti-diffusive terms with the flux limiters is presented.…
The nonlinear convection terms in the governing equations of compressible fluid flows are hyperbolic in nature and are nontrivial for modelling and numerical simulation. Many numerical methods have been developed in the last few decades for…
In this paper, the compressible immiscible two-phase flow with relaxation is investigated, this model can be regarded as a natural modification of Jin-Xin relaxation scheme proposed and developed by S.Jin and Z.P.Xin([Comm.Pure Appl.Math.,…
Quasi-linear hyperbolic systems with source terms introduce significant computational challenges due to the presence of a stiff source term. To address this, a finite volume Nessyahu-Tadmor (NT) central numerical scheme is explored and…
In this work, we introduce a framework to design multidimensional Riemann solvers for nonlinear systems of hyperbolic conservation laws on general unstructured polygonal Voronoi-like tessellations. In this framework we propose two simple…
This work uses a linear relaxation method to develop efficient numerical schemes for the time-fractional Allen-Cahn and Cahn-Hilliard equations. The L1+-CN formula is used to discretize the fractional derivative, and an auxiliary variable…
In this paper, we consider numerical approximations for the viscous Cahn-Hilliard equation with hyperbolic relaxation. This type of equations processes energy-dissipative structure. The main challenge in solving such a diffusive system…
We present a robust computational framework for the numerical solution of a hyperbolic 6-equation single-velocity two-phase system. The system's main interest is that, when combined with instantaneous mechanical relaxation, it recovers the…
This paper is concerned with the numerical solution of the unified first order hyperbolic formulation of continuum mechanics recently proposed by Peshkov & Romenski, denoted as HPR model. In that framework, the viscous stresses are computed…
A numerical scheme of relaxation type is proposed to approximate hyperbolic conservation laws in canal networks. Physical conditions at the junction are given and a novel strategy based on [Briani, Natalini, Ribot, 2025] is introduced to…
This article deals with relaxation approximations of nonlinear systems of hyperbolic balance laws. We introduce a class of relaxation schemes and establish their stability and convergence to the solution of hyperbolic balance laws before…
We develop high-order numerical schemes to solve random hyperbolic conservation laws using linear programming. The proposed schemes are high-order extensions of the existing first-order scheme introduced in [{\sc S. Chu, M. Herty, M.…
This paper presents a geometric variational discretization of compressible fluid dynamics. The numerical scheme is obtained by discretizing, in a structure preserving way, the Lie group formulation of fluid dynamics on diffeomorphism groups…