An accurate, fast, matrix-free implicit method for computing unsteady flows on unstructured grids.

*(English)*Zbl 0983.76056Summary: We develop an accurate, fast, matrix-free implicit method to solve three-dimensional compressible unsteady flows on unstructured grids. A nonlinear system of equations as a result of a fully implicit temporal discretization is solved at each time step using a pseudo-time marching approach. A newly developed method is then used to obtain the steady-state solution to the pseudo-time system. The method is applied to a variety of unsteady flow problems involving moving boundaries. The numerical results obtained indicate that the use of the present implicit method leads to a significant increase in performance over its explicit counterpart, while maintaining a similar memory requirement.

##### Keywords:

matrix-free implicit method; three-dimensional compressible unsteady flows; unstructured grids; pseudo-time marching approach; pseudo-time system; moving boundary
PDF
BibTeX
XML
Cite

\textit{H. Luo} et al., Comput. Fluids 30, No. 2, 137--159 (2001; Zbl 0983.76056)

Full Text:
DOI

##### References:

[1] | Pulliam TH. Time accuracy and the use of implicit schemes. AIAA Paper 93-3360, 1993 |

[2] | Rai MM. Navier-Stokes simulations of blade – vortex interaction using high-order accurate upwind schemes. AIAA Paper 87-0543, January 1987 |

[3] | Brennis, A.; Eberle, A., Application of an implicit relaxation method solving the Euler equations for time-accurate unsteady problems, Transaction of AMSE J. fluids engrg, 112, 510-520, (1990) |

[4] | Jameson A. Time-dependent calculations using multigrid, with application to unsteady flows past airfoils and wings. AIAA Paper 91-1569, July 1991 |

[5] | Vassberg JC. A fast, implicit unstructured-mesh Euler method. AIAA Paper 92-2693, 1992 |

[6] | Crumpton PI, Giles MB. Implicit time accurate solutions on unstructured dynamic grids. AIAA Paper 95-1671, 1995 |

[7] | Venkatakrishnan V, Mavriplis DJ. Implicit method for the computation of unsteady flows on unstructured grids. AIAA Paper 95-1705, 1995 |

[8] | Luo, H.; Baum, J.D.; Löhner, R., A fast, matrix-free implicit method for compressible flows on unstructured grid, Journal of computational physics, 146, 664-690, (1998) · Zbl 0931.76045 |

[9] | Liou MS. Progress towards an improved CFD method: AUSM+. AIAA Paper 95-1701, June 1995 |

[10] | Van Leer, B., Towards the ultimate conservative difference scheme. part II: monotonicity and conservation combined in a second-order scheme, Journal of computational physics, 14, 361-370, (1974) · Zbl 0276.65055 |

[11] | Men’shov, I.; Nakamura, Y., An implicit advection upwind splitting scheme for hypersonic air flows in thermochemical nonequilibrium, () |

[12] | Sharov D, Nakahashi K. Reordering of 3D hybrid unstructured grids for vectorized LU-SGS Navier-Stokes computations. AIAA Paper 97-2102, 1997 |

[13] | Landon H. Compendium of unsteady aerodynamic measurements. AGARD Report No. 702, 1983 |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.