2008 article

Fast p-multigrid discontinuous Galerkin method for compressible flows at all speeds

Luo, H., Baum, J. D., & Lohner, R. (2008, March). AIAA JOURNAL, Vol. 46, pp. 635–652.

co-author countries: United States of America 🇺🇸
Source: Web Of Science
Added: August 6, 2018

Ap-multigrid (wherep is the polynomial degree) discontinuous Galerkin method is presented for the solution of the compressible Euler equations on unstructured grids. The method operates on a sequence of solution approximations of different polynomial orders. A distinct feature ofthisp-multigrid method is the application of an explicit smoother on the higher-level approximations (p > 0) and an implicit smoother on the lowest-level approximation (p = 0), resulting in a fast (and low) storage method that can be efficiently used to accelerate the convergence to a steady-state solution. Furthermore, this p-multigrid method can be naturally applied to compute the flows with discontinuities, in which a monotonic limiting procedure is usually required for discontinuous Galerkin methods. An accurate representation of the boundary normals based on the definition of the geometries is used for imposing slip boundary conditions for curved geometries [Krivodonova, L., and Berger, M., High-Order Implementation of Solid Wall Boundary Conditions in Curved Geometries, Journal of Computational Physics, Vol. 211, No.2,2006, pp. 492-512; and Luo, H., Baum, J. D., and Lohner, R., On the Computation of Steady-State Compressible Flows Using a Discontinuous Galerkin Method, International Journal for Numerical Methods in Engineering, Vol. 73, No.5,2008, pp. 597-623]. A variety of compressible flow problems for a wide range of flow conditions from low Mach number to supersonic in both two-dimensional and three-dimensional configurations are computed to demonstrate the performance ofthisp-multigrid method. The numerical results obtained strongly indicate the order-independent property of this p-multigrid method and demonstrate that this method is orders-of-magnitude faster than its explicit counterpart The performance comparison with a finite volume method shows that using this p-multigrid method, the discontinuous Galerkin method, provides a viable, attractive, competitive, and probably even superior alternative to the finite volume method for computing compressible flows at all speeds.