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Title: Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach

Abstract

Here, a hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P, promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy.

Authors:
 [1]
  1. Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Publication Date:
Research Org.:
Sandia National Lab. (SNL-NM), Albuquerque, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1465806
Report Number(s):
SAND-2017-10354J
Journal ID: ISSN 0021-9991; 666503; TRN: US1902560
Grant/Contract Number:  
AC04-94AL85000
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Journal of Computational Physics
Additional Journal Information:
Journal Volume: 359; Journal Issue: C; Journal ID: ISSN 0021-9991
Publisher:
Elsevier
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Control volume finite element; Discontinuous Galerkin; Higher-order; Sliding mesh; Non-conformal

Citation Formats

Domino, Stefan P. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach. United States: N. p., 2018. Web. doi:10.1016/j.jcp.2018.01.007.
Domino, Stefan P. Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach. United States. doi:10.1016/j.jcp.2018.01.007.
Domino, Stefan P. Fri . "Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach". United States. doi:10.1016/j.jcp.2018.01.007. https://www.osti.gov/servlets/purl/1465806.
@article{osti_1465806,
title = {Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach},
author = {Domino, Stefan P.},
abstractNote = {Here, a hybrid, design-order sliding mesh algorithm, which uses a control volume finite element method (CVFEM), in conjunction with a discontinuous Galerkin (DG) approach at non-conformal interfaces, is outlined in the context of a low-Mach fluid dynamics equation set. This novel hybrid DG approach is also demonstrated to be compatible with a classic edge-based vertex centered (EBVC) scheme. For the CVFEM, element polynomial, P, promotion is used to extend the low-order P = 1 CVFEM method to higher-order, i.e., P = 2. An equal-order low-Mach pressure-stabilized methodology, with emphasis on the non-conformal interface boundary condition, is presented. A fully implicit matrix solver approach that accounts for the full stencil connectivity across the non-conformal interface is employed. A complete suite of formal verification studies using the method of manufactured solutions (MMS) is performed to verify the order of accuracy of the underlying methodology. The chosen suite of analytical verification cases range from a simple steady diffusion system to a traveling viscous vortex across mixed-order non-conformal interfaces. Results from all verification studies demonstrate either second- or third-order spatial accuracy and, for transient solutions, second-order temporal accuracy.},
doi = {10.1016/j.jcp.2018.01.007},
journal = {Journal of Computational Physics},
issn = {0021-9991},
number = C,
volume = 359,
place = {United States},
year = {2018},
month = {1}
}

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Figures / Tables:

Figure 1 Figure 1: Overview of the conceptual differences between non-conformal and overset methodologies. In the sliding mesh technology, (a), a set of surfaces are defined that form a nonconformal interface while in the overset method, a background mesh is intersected with an overset mesh to remove inactive elements, (b); overlap regionsmore » exist and the combined mesh is shown in (c).« less

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