2024/01/29 by Ian C. T. May, Dongwook Lee, May, Ian C. T. +1
Engineering · #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Fluid Dynamics Simulations and Interactions #Lattice Boltzmann Simulation Studies #Numerical Analysis (math.NA)
paper · pdf · doi:10.48550/arxiv.2401.16543
openalex publication_date 2024/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper presents a fully multidimensional kernel-based reconstruction scheme for finite volume methods applied to systems of hyperbolic conservation laws, with a particular emphasis on the compressible Euler equations. Non-oscillatory reconstruction is achieved through an adaptive order weighted essentially non-oscillatory (WENO-AO) method cast into a form suited to multidimensional reconstruction. A kernel-based approach inspired by radial basis functions (RBF) and Gaussian process (GP) modeling, which we call KFVM-WENO, is presented here. This approach allows the creation of a scheme of arbitrary order of accuracy with simply defined multidimensional stencils and substencils. Furthermore, the fully multidimensional nature of the reconstruction allows for a more straightforward extension to higher spatial dimensions and removes the need for complicated boundary conditions on intermediate quantities in modified dimension-by-dimension methods. In addition, a new simple-yet-effective set of reconstruction variables is introduced, which could be useful in existing schemes with little modification. The proposed scheme is applied to a suite of stringent and informative benchmark problems to demonstrate its efficacy and utility. A highly parallel multi-GPU implementation using Kokkos and the message passing interface (MPI) is also provided.