相关论文: Active flux for ideal magnetohydrodynamics: A posi…

We develop a positivity-preserving (PP) PAMPA (Point-Average-Moment PolynomiAl-interpreted) scheme that enforces a discrete divergence-free (DDF) magnetic field for ideal MHD on Cartesian grids. Extending our 1D invariant-domain-preserving…

The active flux (AF) method is a compact high-order finite volume method that simultaneously evolves cell averages and point values at cell interfaces. Within the method of lines framework, the existing Jacobian splitting-based point value…

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…

The active flux (AF) method is a compact high-order finite volume method that evolves cell averages and point values at cell interfaces independently. Within the method of lines framework, the point value can be updated based on Jacobian…

The Active Flux (AF) method is a compact, high-order finite volume scheme that enhances flexibility by introducing point values at cell interfaces as additional degrees of freedom alongside cell averages. The method of lines is employed…

Active Flux (AF) is a modified Finite Volume method that evolves additional Degrees of Freedom (DoF) located on the cell interfaces to compute high-order approximations to the numerical fluxes through the respective interface. We present an…

The active flux (AF) method is a compact high-order finite volume method originally proposed for solving hyperbolic conservation laws, in which cell averages and point values at cell interfaces are evolved simultaneously. This paper…

This paper proposes and analyzes a novel efficient high-order finite volume method for the ideal magnetohydrodynamics (MHD). As a distinctive feature, the method simultaneously preserves a discretely divergence-free (DDF) constraint on the…

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 show how to combine in a natural way (i.e. without any test nor switch) the conservative and non conservative formulations of an hyperbolic system that has a conservative form. This is inspired from two different class of schemes: the…

In this work, we present a positivity-preserving adaptive filtering approach for discontinuous spectral element approximations of the ideal magnetohydrodynamics equations. This approach combines the entropy filtering method (Dzanic and…

Numerical schemes provably preserving the positivity of density and pressure are highly desirable for MHD, but the rigorous positivity-preserving (PP) analysis remains challenging. The difficulties mainly arise from the intrinsic complexity…

This paper studies the active flux (AF) methods for two-dimensional hyperbolic conservation laws, focusing on the flux vector splitting (FVS) for the point value update and bound-preserving (BP) limitings, which is an extension of our…

The Active Flux method is a numerical method for conservation laws using a combination of cell averages and point values, based on ideas from finite volumes and finite differences. This unusual mix has been shown to work well in many…

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…

This paper proposes and analyzes arbitrarily high-order discontinuous Galerkin (DG) and finite volume methods which provably preserve the positivity of density and pressure for the ideal MHD on general meshes. Unified auxiliary theories are…

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…

Active Flux is a modified Finite Volume method that evolves additional Degrees of Freedom for each cell that are located on the interface by a non-conservative method to compute high-order approximations to the numerical fluxes through the…

We develop a new second-order flux globalization based path-conservative central-upwind (PCCU) scheme for rotating shallow water magnetohydrodynamic equations. The new scheme is designed not only to maintain the divergence-free constraint…

We develop a new numerical scheme for ideal magnetohydrodynamic (MHD) simulations, which is robust against one- and multi-dimensional shocks, and is accurate for low Mach number flows and discontinuities. The scheme belongs to a family of…