High-order discontinuous Galerkin methods with finite volume subcells for compressible flows on simplices

This work presents GPU-accelerated nodal discontinuous Galerkin methods for supersonic and hypersonic flows with finite volume subcell stabilization on simplices. Our approach merges the favorable attributes of the discontinuous Galerkin method in smooth flow regions with the ideal characteristics of a total variation diminishing finite volume methods for resolving shocks. A modal decay rate-based regularity estimator is used to detect high-wavenumber solution components near shocks and under-resolved regions. The methodology is implemented in the libParanumal library which includes a set of finite element flow solvers for heterogeneous (GPU/CPU) systems through OCCA, an open-source library that provides the portability layer to offload targeted kernels across different architectures and vendor platforms. The efficiency, scalability, and local high-order accuracy of the method are confirmed through distinct supersonic and hypersonic test cases. The kernel performance metrics will be demonstrated for various GPU architectures, including NVIDIA, Intel, and AMD GPUs, as well as for different programming models, CUDA, OpenCL, and SYCL.