Variable High-Order Shock Capturing with GP-WENO in the FLASH Code

We present an implementation of a shock-capturing scheme for hyperbolic equations. The method attains high-order of accuracy by using kernel-based Gaussian process (GP) data prediction for the reconstruction of Riemann states in a finite volume framework. To handle shocks and discontinuities the method adopts a strategy similar to the weighted essentially non-oscillatory (WENO) schemes. In GP-WENO the GP prediction takes place of the polynomial interpolation and the conventional $L_2$ type WENO smoothness indicators are replaced with the Gaussian likelihood derived from the underlying GP model. The new GP smoothness indicators provide significant improvements in delivering a selectable high-order accuracy in smooth flows, while giving non-oscillatory solutions in discontinuous flows. We benchmark GP-WENO on a suite of test problems using an implementation in the FLASH code. This addition promises a significant enhancement to the code’s fidelity in modeling laser-driven plasma experiments.