High-order finite-volume adaptive methods on locally rectangular grids

High-order finite-volume adaptive methods on locally rectangular grids

We are developing a new class of finite-volume methods on locally-refined and mapped grids, which are at least fourth-order accurate in regions where the solution is smooth. This paper discusses the implementation of such methods for time-dependent problems on both Cartesian and mapped grids with adaptive mesh refinement. We show 2D results with the Berger–Colella shock-ramp problem in Cartesia...

High-Order Finite-Volume Methods on Locally-Structured Grids

For many problems in astrophysics and space sciences, it is desirable to compute solutions in a way that preserves spherical symmetry, so that the dynamics of small perturbations about the spherically symmetric case are not overwhelmed by numerical error. Traditionally, such calculations have been done by discretizing the equations expressed in spherical coordinates. This approach has significa...

A High-order Finite-volume Method for Conservation Laws on Locally Refined Grids

Improved Accuracy of High-Order WENO Finite Volume Methods on Cartesian Grids

We will present our recent result on the construction of high order WENO finite volume methods for the approximation of hyperbolic partial differential equations on Cartesian grids. The simplest way to use WENO methods on multidimensional Cartesian grids consists in applying a one-dimensional WENO scheme in each direction. This spatial discretization is typically combined with a Runge-Kutta met...

High-order finite-volume methods for hyperbolic conservation laws on mapped multiblock grids

We present an approach to solving hyperbolic conservation laws by finitevolume methods on mapped multiblock grids, extending the approach of Colella, Dorr, Hittinger, and Martin (2011) for grids with a single mapping. We consider mapped multiblock domains for mappings that are conforming at inter-block boundaries. By using a smooth continuation of the mapping into ghost cells surrounding a bloc...