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In this paper, we introduce a novel approach that combines multiresolution(MR) techniques with the flux reconstruction (FR) method to accurately andeffciently simulate compressible flows. We achieve further enhancements ineffciency through the incorporation of local time stepping, and we addartificial viscosity to capture shocks. With the developed MR-FR algorithm, thelayer difference of two adjacent elements can exceed 1, and simulation errorscan be adjusted by manipulating a single scalar. To ensure conservation,information communication between nodes at different layers is accomplishedusing L2 projection. Additionally, we propose an innovative indicator based onMR analysis to detect discontinuities, enabling us to take full advantage ofthe details generated by MR. By indicating smoothness and adding artificialviscosity only to the finest meshes, computational costs can be reduced anderrors resulting from artificial diffusion can be locally limited. Numericaltests demonstrate that the adoption of MR preserve the convergence order of theFR method, and the newly proposed indicator performs well in detectingdiscontinuities. Overall, the MR-FR algorithm can accurately simulatecompressible flows with strong shocks and physical dissipation usingsignificantly fewer grids, making it a promising approach for furtherapplications.

An adaptive multiresolution flux reconstruction method with local time stepping and artificial viscosity for compressible flows simulations