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Adaptive mesh refinement on graphics processing units for applications in gas dynamics. (English) Zbl 1451.65139
Summary: We present novel algorithms for cell-based adaptive mesh refinement on unstructured meshes of triangles on graphics processing units. Our implementation makes use of improved memory management techniques and a coloring algorithm for avoiding race conditions. Both the solver and AMR algorithms are entirely implemented on the GPU, with negligible communication between device and host. We show that the overhead of the AMR subroutines is small compared to the high order solver and that the proportion of total runtime spent adaptively refining the mesh decreases with the order of approximation. We apply our code to a number of benchmark problems as well as more recently proposed problems for the Euler equations that require extremely high resolution. We present the solution to a shock reflection problem that addresses the von Neumann triple point paradox with an accurately computed triple point location. Finally, we present the first solution on the full Euler equations to the problem of shock disappearance and self-similar diffraction of weak shocks around thin films.
MSC:
65M50 Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs
65M60 Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs
76M10 Finite element methods applied to problems in fluid mechanics
35L65 Hyperbolic conservation laws
65Y20 Complexity and performance of numerical algorithms
76N15 Gas dynamics, general
65Y05 Parallel numerical computation
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