GP-MOOD: A positive-preserving high-order finite volume method for hyperbolic conservation laws

Abstract

We present an a posteriori shock-capturing finite volume method algorithm called GP-MOOD that solves a compressible hyperbolic conservative system at high-order solution accuracy (e.g., third-, fifth-, and seventh-order) in multiple spatial dimensions. The GP-MOOD method combines two methodologies, the polynomial-free spatial reconstruction methods of GP (Gaussian Process) and the a posteriori detection algorithms of MOOD (Multidimensional Optimal Order Detection). The spatial approximation of our GP-MOOD method uses GP's unlimited spatial reconstruction that builds upon our previous studies on GP reported in Reyes et al.,