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Title: High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics

Abstract

We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification ofmore » the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10-5, which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM + -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.« less

Authors:
ORCiD logo [1]; ORCiD logo [1];  [1];  [1];  [1];  [1]; ORCiD logo [2]
  1. Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States). Design Physics Dept.
  2. Univ. of California, Davis, CA (United States)
Publication Date:
Research Org.:
Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)
Sponsoring Org.:
USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1562804
Report Number(s):
LLNL-JRNL-745590
Journal ID: ISSN 0938-1287; 900894
Grant/Contract Number:  
AC52-07NA27344
Resource Type:
Journal Article: Accepted Manuscript
Journal Name:
Shock Waves
Additional Journal Information:
Journal Volume: 29; Journal Issue: 5; Journal ID: ISSN 0938-1287
Publisher:
Springer
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; reconstructed/recovery discontinuous Galerkin method; all-speed AUSM+-up scheme; fully implicit; Jacobian-free Newton-Krylov; preconditioning

Citation Formats

Nourgaliev, R., Greene, P., Weston, B., Barney, R., Anderson, A., Khairallah, S., and Delplanque, J. -P. High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics. United States: N. p., 2018. Web. doi:10.1007/s00193-018-0871-8.
Nourgaliev, R., Greene, P., Weston, B., Barney, R., Anderson, A., Khairallah, S., & Delplanque, J. -P. High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics. United States. doi:10.1007/s00193-018-0871-8.
Nourgaliev, R., Greene, P., Weston, B., Barney, R., Anderson, A., Khairallah, S., and Delplanque, J. -P. Wed . "High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics". United States. doi:10.1007/s00193-018-0871-8. https://www.osti.gov/servlets/purl/1562804.
@article{osti_1562804,
title = {High-order fully implicit solver for all-speed fluid dynamics: AUSM ride from nearly incompressible variable-density flows to shock dynamics},
author = {Nourgaliev, R. and Greene, P. and Weston, B. and Barney, R. and Anderson, A. and Khairallah, S. and Delplanque, J. -P.},
abstractNote = {We introduce a novel Newton–Krylov (NK)-based fully implicit algorithm for solving fluid flows in a wide range of flow conditions—from variable density nearly incompressible to supersonic shock dynamics. The key enabling feature of our all-speed solver is the ability to efficiently solve conservation laws by choosing a set of independent variables that produce a well-conditioned Jacobian matrix for the linear iterations of the global nonlinear iterative solver. In particular, instead of choosing to discretize the conservative variables (density, momentum, total energy), which is traditionally used in Eulerian high-speed compressible fluid dynamics, we demonstrate superior performance by discretizing the primitive variables—pressure–velocity–temperature in the very low-Mach flow limits or density–velocity–temperature/entropy in the shock dynamics range. Moreover, our method allows us to avoid direct inversion of the mass matrix in discrete time derivatives, which is usually an additional source for stiffness, especially pronounced when going to very high-order schemes with non-orthogonal basis functions. Here, we show robust solutions obtained for discontinuous finite element discretization up to seventh-order accuracy. Another important aspect of the solution algorithm is the Advection Upstream Splitting Method (AUSM), adopted to compute numerical fluxes within our reconstructed discontinuous Galerkin (rDG) spatial discretization scheme. The use of the low-Mach modification of the hyperbolic flux operator is found to be necessary for enabling robust simulations of very stiff liquids and metals for Mach numbers below M=10-5, which is well known to be very computationally challenging for compressible solvers. We demonstrate that our fully implicit rDG-NK solver with the AUSM+ -up flux treatment produces efficient and high-resolution numerical solutions at all speeds, ranging from vanishing Mach numbers to transonic and supersonic, without substantial modifications of the solution procedures. (At high speed, we add limiting and use a simpler preconditioning of the Krylov solver.) Numerical examples include nearly incompressible constant-property flow past a backward-facing step with heat transfer, low-Mach variable-property channel flow of water at supercritical state, phase change and melt pool dynamics for laser spot welding and selective laser melting in additive manufacturing, and Mach 3 flow in a wind tunnel with a step.},
doi = {10.1007/s00193-018-0871-8},
journal = {Shock Waves},
issn = {0938-1287},
number = 5,
volume = 29,
place = {United States},
year = {2018},
month = {11}
}

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