Related papers: The Cartesian Grid Active Flux Method with Adaptiv…
Finite volume schemes for hyperbolic conservation laws require a numerical intercell flux. In one spatial dimension the numerical flux can be successfully obtained by solving (exactly or approximately) Riemann problems that are introduced…
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…
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…
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 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…
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…
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…
Active Flux is a third order accurate numerical method which evolves cell averages and point values at cell interfaces independently. It naturally uses a continuous reconstruction, but is stable when applied to hyperbolic problems. In this…
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 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 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 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…
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…
We propose a simple modification of standard WENO finite volume methods for Cartesian grids, which retains the full spatial order of accuracy of the one-dimensional discretization when applied to nonlinear multidimensional systems 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…
Three algebraically stabilized finite element schemes for discretizing convection-diffusion-reaction equations are studied on adaptively refined grids. These schemes are the algebraic flux correction (AFC) scheme with Kuzmin limiter, the…
We present a non-staggered method for the Maxwell equations in adaptively refined grids. The code is based on finite volume central scheme that preserves in a discrete form both divergence-free property of magnetic field and the Gauss law.…
We describe a parallel, adaptive, multi-block algorithm for explicit integration of time dependent partial differential equations on two-dimensional Cartesian grids. The grid layout we consider consists of a nested hierarchy of fixed size,…
For accurate simulations of rarefied gas flows around moving obstacles, we propose a cut cell method on Cartesian grids: it allows exact conservation and accurate treatment of boundary conditions. Our approach is designed to treat Cartesian…
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…