Brinkman Penalization and Boundary Layer in High-Order Discontinuous Galerkin

Neda Ebrahimi Pour (), Nikhil Anand (), Felix Bernhards, Harald Klimach () and Sabine Roller ()
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Neda Ebrahimi Pour: University of Siegen
Nikhil Anand: University of Siegen
Felix Bernhards: University of Siegen
Harald Klimach: University of Siegen
Sabine Roller: University of Siegen

A chapter in Sustained Simulation Performance 2019 and 2020, 2021, pp 85-94 from Springer

Abstract: Abstract In this chapter we look into a high-order representation of complex geometries by the Brinkman penalization method. We focus on the effect of this immersed boundary model on the boundary layers in a high-order discontinuous Galerkin scheme. High-order approximations are attractive on modern computing architectures, as they require few degrees of freedom, to represent smooth solutions, resulting in a smaller memory footprint when compared to lower order discretizations. A significant hurdle in using high-order methods for problems involving complex geometries is matching the surface description of the geometry with the discretization scheme. The Brinkman penalization offers a method to achieve this without the need for complicated mesh generation and special elements. We investigated its use in our high-order discontinuous Galerkin implementation Ateles in [2], where we looked at inviscid effects like reflections. Here we investigate the viscous boundary layer close to a wall, modeled by the penalization.

Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-68049-7_6

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DOI: 10.1007/978-3-030-68049-7_6

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