Block-Structured Adaptive Mesh Refinement Algorithms for Vlasov Simulation

TL;DR

This paper introduces advanced block-structured adaptive mesh refinement algorithms tailored for high-dimensional Vlasov simulations, enabling more efficient computation by handling multi-dimensional data transfer and high-order discretizations.

Contribution

It develops novel algorithms for multi-dimensional data transfer in AMR and extends high-order discretization techniques to Vlasov simulations.

Findings

Preliminary results show potential for significant computational savings.

Algorithms effectively handle variable dimensions in mesh hierarchies.

High-order discretizations improve accuracy in Vlasov simulations.

Abstract

Direct discretization of continuum kinetic equations, like the Vlasov equation, are under-utilized because the distribution function generally exists in a high-dimensional (>3D) space and computational cost increases geometrically with dimension. We propose to use high-order finite-volume techniques with block-structured adaptive mesh refinement (AMR) to reduce the computational cost. The primary complication comes from a solution state comprised of variables of different dimensions. We develop the algorithms required to extend standard single-dimension block structured AMR to the multi-dimension case. Specifically, algorithms for reduction and injection operations that transfer data between mesh hierarchies of different dimensions are explained in detail. In addition, modifications to the basic AMR algorithm that enable the use of high-order spatial and temporal discretizations are discussed. Preliminary results for a standard 1D+1V Vlasov-Poisson test problem are presented. Results indicate that there is potential for significant savings for some classes of Vlasov problems.