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An Implicit Algorithm for High-Order DG/FV Schemes for Compressible Flows on 2D Arbitrary Grids

Published online by Cambridge University Press:  19 December 2014

Laiping Zhang ,
Ming Li ,
Wei Liu  and
Xin He
Laiping Zhang*
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan, 621000, China China Aerodynamics Research and Development Center, Mianyang, Sichuan, 621000, China
Ming Li
Affiliation:
China Aerodynamics Research and Development Center, Mianyang, Sichuan, 621000, China
Wei Liu
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan, 621000, China China Aerodynamics Research and Development Center, Mianyang, Sichuan, 621000, China
Xin He
Affiliation:
State Key Laboratory of Aerodynamics, Mianyang, Sichuan, 621000, China
*
*Email addresses: zhanglp_cardc@126.com (L. Zhang), mli@sina.com (M. Li), lw4992@gmail.com (W. Liu), fantasy2003@gmail.com (X. He)
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Abstract

A Newton/LU-SGS (lower-upper symmetric Gauss-Seidel) iteration implicit method was developed to solve two-dimensional Euler and Navier-Stokes equations by the DG/FV hybrid schemes on arbitrary grids. The Newton iteration was employed to solve the nonlinear system, while the linear system was solved with LU-SGS iteration. The effect of several parameters in the implicit scheme, such as the CFL number, the Newton sub-iteration steps, and the update frequency of Jacobian matrix, was investigated to evaluate the performance of convergence history. Several typical test cases were simulated, and compared with the traditional explicit Runge-Kutta (RK) scheme. Firstly the Couette flow was tested to validate the order of accuracy of the present DG/FV hybrid schemes. Then a subsonic inviscid flow over a bump in a channel was simulated and the effect of parameters was investigated also. Finally, the implicit algorithm was applied to simulate a subsonic inviscid flow over a circular cylinder and the viscous flow in a square cavity. The numerical results demonstrated that the present implicit scheme can accelerate the convergence history efficiently. Choosing proper parameters would improve the efficiency of the implicit scheme. Moreover, in the same framework, the DG/FV hybrid schemes are more efficient than the same order DG schemes.

Keywords

65C2065L6065M0865M6068U2076M1076M12Implicit algorithmdiscontinuous Galerkin methodDG/FV hybrid SchemeNewton iterationGauss-Seidel iteration

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Type
Research Article
Information
Communications in Computational Physics , Volume 17 , Issue 1 , January 2015 , pp. 287 - 316
Copyright
Copyright © Global Science Press Limited 2015 

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