A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods

Rueda-Ramirez, Andres M. and Manzanero Torrico, Juan and Ferrer Vaccarezza, Esteban and Rubio Calzado, Gonzalo and Valero Sanchez, Eusebio (2019). A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods. "Journal of Computational Physics", v. 378 ; pp. 209-233. ISSN 0021-9991. https://doi.org/10.1016/j.jcp.2018.11.009.

Description

Title: A p-multigrid strategy with anisotropic p-adaptation based on truncation errors for high-order discontinuous Galerkin methods
Author/s:
  • Rueda-Ramirez, Andres M.
  • Manzanero Torrico, Juan
  • Ferrer Vaccarezza, Esteban
  • Rubio Calzado, Gonzalo
  • Valero Sanchez, Eusebio
Item Type: Article
Título de Revista/Publicación: Journal of Computational Physics
Date: 2019
ISSN: 0021-9991
Volume: 378
Subjects:
Freetext Keywords: High-order discontinuous Galerkin; Anisotropic p-adaptation; Error estimation; p-Multigrid; Compressible flows
Faculty: E.T.S. de Ingeniería Aeronáutica y del Espacio (UPM)
Department: Matemática Aplicada a la Ingeniería Aeroespacial
Creative Commons Licenses: Recognition - No derivative works - Non commercial

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Abstract

High-order discontinuous Galerkin methods have become a popular technique in computational fluid dynamics because their accuracy increases spectrally in smooth solutions with the order of the approximation. However, their main drawback is that increasing the order also increases the computational cost. Several techniques have been introduced in the past to reduce this cost. On the one hand, local mesh adaptation strategies based on error estimation have been proposed to reduce the number of degrees of freedom while keeping a similar accuracy. On the other hand, multigrid solvers may accelerate time marching computations for a fixed number of degrees of freedom. In this paper, we combine both methods and present a novel anisotropic p-adaptation multigrid algorithm for steady-state problems that uses the multigrid scheme both as a solver and as an anisotropic error estimator. To achieve this, we show that a recently developed anisotropic truncation error estimator [1, A. M. Rueda-Ramírez, G. Rubio, E. Ferrer, E. Valero, Truncation error estimation in the p-anisotropic discontinuous Galerkin spectral element method, J. Sci. Comput.] is perfectly suited to be performed inside the multigrid cycle with negligible extra cost. Furthermore, we introduce a multi-stage p-adaptation procedure which reduces the computational time when very accurate results are required. The proposed methods are tested for the compressible Navier–Stokes equations, where we investigate two steady-state cases. First, the 2D boundary layer flow on a flat plate is studied to assess accuracy and computational cost of the algorithm, where a speed-up of 816 is achieved compared to the traditional explicit method. Second, the 3D flow around a sphere is simulated and used to test the anisotropic properties of the proposed method, where a speed-up of 152 is achieved compared to the explicit method. The proposed multi-stage procedure achieved a speed-up of 2.6 in comparison to the single-stage method in highly accurate simulations.

Funding Projects

TypeCodeAcronymLeaderTitle
Government of SpainTRA2015-67679-C2-2-RUnspecifiedUnspecifiedEstudio de la interacción chorro-pared en condiciones realistas de motor

More information

Item ID: 67107
DC Identifier: https://oa.upm.es/67107/
OAI Identifier: oai:oa.upm.es:67107
DOI: 10.1016/j.jcp.2018.11.009
Official URL: https://www.sciencedirect.com/science/article/pii/S0021999118307277
Deposited by: Memoria Investigacion
Deposited on: 20 Dec 2021 10:24
Last Modified: 20 Dec 2021 10:24
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