On differentiable local bounds preserving stabilization for Euler equations

Badia, Santiago; Bonilla, Jesús; Mabuza, Sibusiso; Shadid, John N.

doi:10.1016/j.cma.2020.113267

On differentiable local bounds preserving stabilization for Euler equations

Journal Article · 01 October 2020 · Computer Methods in Applied Mechanics and Engineering

DOI:https://doi.org/10.1016/j.cma.2020.113267· OSTI ID:1639088

Badia, Santiago ^[1]; Bonilla, Jesús ^[2]; Mabuza, Sibusiso ^[3]; Shadid, John N. ^[4]

Monash Univ., Clayton, VIC (Australia); Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Castelldefels (Spain)
Centre Internacional de Mètodes Numèrics en Enginyeria (CIMNE), Castelldefels (Spain); Univ. Politecnica de Catalunya, Barcelona (Spain)
Clemson Univ., SC (United States)
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States). Center for Computing Research; Univ. of New Mexico, Albuquerque, NM (United States)

This work presents the design of nonlinear stabilization techniques for the finite element discretization of Euler equations in both steady and transient form. Implicit time integration is used in the case of the transient form. A differentiable local bounds preserving method has been developed, which combines a Rusanov artificial diffusion operator and a differentiable shock detector. Nonlinear stabilization schemes are usually stiff and highly nonlinear. This issue is mitigated by the differentiability properties of the proposed method. Moreover, in order to further improve the nonlinear convergence, we also propose a continuation method for a subset of the stabilization parameters. The resulting method has been successfully applied to steady and transient problems with complex shock patterns. Numerical experiments show that it is able to provide sharp and well resolved shocks. Furthermore, the importance of the differentiability is assessed by comparing the new scheme with its non-differentiable counterpart. Numerical experiments suggest that, for up to moderate nonlinear tolerances, the method exhibits improved robustness and nonlinear convergence behavior for steady problems. Additionally, in the case of transient problem, we also observe a reduction in the computational cost.

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Research Organization:: Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)

Sponsoring Organization:: USDOE Office of Science (SC), Advanced Scientific Computing Research (ASCR); La Caixa Foundation; USDOE

Grant/Contract Number:: AC04-94AL85000; NA0003525; LCF/BQ/DE15/10360010

OSTI ID:: 1639088

Alternate ID(s):: OSTI ID: 1637576

Report Number(s):: SAND-2020-6831J; 687134

Journal Information:: Computer Methods in Applied Mechanics and Engineering, Vol. 370; ISSN 0045-7825

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

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