Related papers: Arbitrary order finite volume well-balanced scheme…
We propose an arbitrarily high-order accurate, fully well-balanced numerical method for the one-dimensional blood flow model. The developed method employs a continuous solution representation, combining conservative and primitive…
We develop arbitrarily high-order, stationarity-preserving stabilized finite element methods for multidimensional nonlinear hyperbolic balance laws on Cartesian grids. We aim at approximating all the steady states of the problem at hand,…
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…
In this paper, a centred universal high-order finite volume method for solving hyperbolic balance laws is presented. The scheme belongs to the family of ADER methods where the Generalized Riemann Problems (GRP) is a building block. The…
We present an implicit-explicit finite volume scheme for the Euler equations. We start from the non-dimensionalised Euler equations where we split the pressure in a slow and a fast acoustic part. We use a Suliciu type relaxation model which…
The development of a set of high-order accurate finite-volume formulations for evaluation of the pressure gradient force in layered ocean models is described. A pair of new schemes are presented, both based on an integration of the contact…
In this paper, we present a class of finite volume schemes for incompressible flow problems. The unknowns are collocated at the center of the control volumes, and the stability of the schemes is obtained by adding to the mass balance…
In this paper, we design a novel class of arbitrarily high-order structure-preserving numerical schemes for the time-dependent Gross-Pitaevskii equation with angular momentum rotation in three dimensions. Based on the idea of the scalar…
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…
High order algorithms have emerged in numerical astrophysics as a promising avenue to reduce truncation error (proportional to a power of the linear resolution $\Delta x$) with only a moderate increase to computational expense. Significant…
We consider the relativistic Euler equations governing spherically symmetric, perfect fluid flows on the outer domain of communication of Schwarzschild spacetime, and we introduce a version of the finite volume method which is formulated…
We propose a new finite volume scheme for the Euler system of gas dynamics motivated by the model proposed by H. Brenner. Numerical viscosity imposed through upwinding acts on the velocity field rather than on the convected quantities. The…
In this paper, high order well-balanced finite difference weighted essentially non-oscillatory methods to solve general systems of balance laws are presented. Two different families are introduced: while the methods in the first one…
This paper focusses on finite volume schemes for solving multilayer diffusion problems. We develop a finite volume method that addresses a deficiency of recently proposed finite volume/difference methods, which consider only a limited…
In the present work, a high order finite element type residual distribution scheme is designed in the framework of multidimensional compressible Euler equations of gas dynamics. The strengths of the proposed approximation rely on the…
In some previous works, two of the authors have introduced a strategy to develop high-order numerical methods for systems of balance laws that preserve all the stationary solutions of the system. The key ingredient of these methods is a…
In this work, we present a high-order finite volume framework for the numerical simulation of shallow water flows. The method is designed to accurately capture complex dynamics inherent in shallow water systems, particularly suited for…
The present work proposes a well-balanced finite volume-type numerical method for the solution of non-conservative hyperbolic partial differential equations (PDEs) with source terms. The method is characterized, first, by the use of a…
In this paper we propose a novel second-order accurate well balanced scheme for shallow water equations in general covariant coordinates over manifolds. In our approach, once the gravitational field is defined for the specific case, one…
In some previous works, two of the authors introduced a technique to design high-order numerical methods for one-dimensional balance laws that preserve all their stationary solutions. The basis of these methods is a well-balanced…