Adaptive finite-volume WENO schemes on dynamically redistributed grids for compressible Euler equations

摘要: A high-order adaptive finite-volume method is presented for simulating inviscid compressible flows on time-dependent redistributed grids. The achieves dynamic adaptation through a combination of mesh node clustering in regions characterized by strong solution gradients and an optimal selection the order accuracy associated reconstruction stencil conservative framework. This combined approach maximizes spatial resolution discontinuous that require low-order approximations oscillation-free shock capturing. Over smooth regions, discretization WENO schemes minimizes numerical dissipation provides excellent intricate flow features. including moving equations solver formulated entirely transformed time-independent computational domain discretized using simple uniform Cartesian mesh. Approximations metric terms enforce discrete geometric conservation law while preserving fourth-order two-point Gaussian quadrature rule are developed. Spurious grid induced instabilities such as carbuncles feature local one-dimensional contact capturing treatment along cell face normals effectively eliminated upwind flux calculation rotated Hartex-Lax-van Leer resolving (HLLC) approximate Riemann Euler generalized coordinates. Numerical experiments with fifth ninth-order reconstructions at nodes, over range challenging test cases, indicate adapts to thereby improving substantially even when initial starting non-adaptive. high adaptivity especially allows remarkably sharp capture propagating shocks simultaneous yet complex small scale unsteady features exceptional detail.