A p-Multigrid Strategy with Anisotropic p-Adaptation Based on Truncation Errors for High-Order Discontinuous Galerkin Methods

摘要: High-order DG methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally smooth solutions with the order of approximation. However, main drawback is that increasing also cost. Several techniques been introduced past to reduce this On one hand, local mesh adaptation strategies based on error estimation proposed number degrees freedom while keeping similar accuracy. other multigrid solvers may accelerate time marching computations for fixed freedom. In paper, we combine both and present novel anisotropic p-adaptation algorithm steady-state problems uses scheme as solver an estimator. To achieve this, show recently developed truncation estimator [\textit{Rueda-Ram\'irez et al., Truncation Error Estimation p-Anisotropic DGSEM, J. Scientific Computing}] perfectly suited be performed inside cycle negligible extra Furthermore, introduce multi-stage procedure which reduces when very accurate results are required. The tested compressible Navier-Stokes equations, where investigate two cases: 2D flow flat plate studied assess cost algorithm, speed-up 816 achieved compared traditional explicit method; 3D around sphere simulated used test properties method, 152 method. 2.6 comparison single-stage method highly simulations.