Related papers: The active flux scheme on Cartesian grids and its …
The Active Flux scheme is a finite volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver. Instead, given a reconstruction, the initial value problem…
The Active Flux scheme is a Finite Volume scheme with additional point values distributed along the cell boundary. It is third order accurate and does not require a Riemann solver: the continuous reconstruction serves as initial data for…
Active Flux is an extension of the Finite Volume method and additionally incorporates point values located at cell boundaries. This gives rise to a globally continuous approximation of the solution. Originally, the Active Flux method…
We present the first implementation of the Active Flux method on adaptively refined Cartesian grids. The Active Flux method is a third order accurate finite volume method for hyperbolic conservation laws, which is based on the use of point…
The Active Flux method is a finite volume method for hyperbolic conservation laws that uses both cell averages and point values as degrees of freedom. Several versions of such methods are currently under development. We focus on third order…
The Active Flux scheme is a Finite Volume scheme with additional degrees of freedom. It makes use of a continuous reconstruction and does not require a Riemann solver. An evolution operator is used for the additional degrees of freedom on…
The Active Flux method can be seen as an extended finite volume method. The degrees of freedom of this method are cell averages, as in finite volume methods, and in addition shared point values at the cell interfaces, giving rise to a…
This work focuses on the numerical solution of hyperbolic conservations laws (possibly endowed with a source term) using the Active Flux method. This method is an extension of the finite volume method. Instead of solving a Riemann Problem,…
Active Flux is a recently developed numerical method for hyperbolic conservation laws. Its classical degrees of freedom are cell averages and point values at cell interfaces. These latter are shared between adjacent cells, leading to a…
An explicit moving boundary method for the numerical solution of time-dependent hyperbolic conservation laws on grids produced by the intersection of complex geometries with a regular Cartesian grid is presented. As it employs directional…
We present a Cartesian cut-cell finite-volume method for sharp-interface two-phase diffusion problems in static geometries. The formulation follows a two-fluid approach: independent diffusion equations are discretized in each phase on a…
In this article, we show how to construct a numerical method for solving hyperbolic problems, whether linear or nonlinear, using a continuous representation of the variables and their mean value in each triangular element. This type of…
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…
A Cartesian grid method combined with a simplified gas kinetic scheme is presented for subsonic and supersonic viscous flow simulation on complex geometries. Under the Cartesian mesh, the computational grid points are classified into four…
In this work we develop implicit Active Flux schemes for the scalar advection equation. At every cell interface we approximate the solution by a polynomial in time. This allows to evolve the point values using characteristics and to update…
We present a dimensionally split method for solving hyperbolic conservation laws on Cartesian cut cell meshes. The approach combines local geometric and wave speed information to determine a novel stabilised cut cell flux, and we provide a…
We construct a new nonlinear finite volume (FV) scheme for highly anisotropic diffusion equations, that satisfies the discrete minimum-maximum principle. The construction relies on the linearized scheme satisfying less restrictive…
The degrees of freedom of Active Flux are cell averages and point values along the cell boundaries. These latter are shared between neighbouring cells, which gives rise to a globally continuous reconstruction. The semi-discrete Active Flux…
Active Flux (AF) is a recent numerical method for hyperbolic conservation laws, whose degrees of freedom are averages/moments and (shared) point values at cell interfaces. It has been noted previously in a heuristic fashion that it thus…
We present well-balanced finite volume schemes designed to approximate the Euler equations with gravitation. They are based on a novel local steady state reconstruction. The schemes preserve a discrete equivalent of steady adiabatic flow,…