The application of the locally implicit method to upwind TVD schemes
Tóm tắt
The local implicit scheme of Reddyet al. is extended to the minmod and third-order upwind TVD schemes. Numerical tests show that the proposed scheme is stable. In addition, it is found that if the flow field has a dominant direction, setting the iteration sweep to align with this direction can significantly improve the converging speed.
Tài liệu tham khảo
Harten, A. (1983). High-resolution schemes for hyperbolic conservations laws,J. Comput. Phys. 49, 357–393.
Hung, C. M. (1987). Extrapolation of velocity for inviscid solid boundary conditions,AIAA J. 25, 1513–1515.
Hwang, C. J., and Liu, J. L. (1991a). Inviscid and viscous solutions for airfoil/cascade flows using a locally implicit algorithm on adaptive meshes,Trans. ASME J. Turbomachinery 113(4), 553–560.
Hwang, C. J., and Liu, J. L. (1991b). Locally implicit total-variation-diminishing schemes on unstructured triangular meshes,AIAA J. 29(10), 1619–1629.
Hwang, C. J., and Liu, J. L. (1992). A locally implicit hybrid algorithm for steady and unsteady viscous flows, to appear inAIAA J.
Jeng, Y. N., Wu, T. J., and Payne, U. J. (1990a). A high-resolution TVD scheme for Euler equations, Proc. of Aero. & Asto. Conf. AASRC, pp. 139–150.
Jeng, Y. N., Wu, T. J., and Payne, U. J. (1990b). A class of high-resolution TVD schemes, The 4th National Conf. on Theor. & Applied Mech., Chung Li, Taiwan, STRAMROC-14-L40.
Munz, C.-D. (1988). On the numerical dissipation of high resolution schemes for hyperbolic conservation laws,J. Comput. Phys. 77, 18–39.
Nayani, S. N. (1988). A locally implicit scheme for Navier-Stokes equations, Ph.D dissertation, The University of Tennesee, Knoxville.
Pulliam, T. H., and Steger, J. (1985). Recent improvements in efficient, accuracy and convergence for implicit factorization algorithms, AIAA-85-0360.
Reddy, K. C., and Jacocks, J. L. (1987). A locally implicit scheme for the Euler equations, AIAA-87-1144, Proceedings of 8th CFD Conference, Honolulu.
Steger, J. L., and Sorenson, R. L. (1979). Automatic mesh-point clustering near a boundary in grid generation with elliptic partial differential equations,J. Comput. Phys. 33, 405–410.
Sweby, P. K. (1984). High-resolution schemes using flux limiters for hyperbolic conservation laws,SIAM J. Numer. Anal. 21, 995–1011.
Yang, H., and Przekwas, A. (1990). A comparative study of advanced shock-capturing schemes applied to Burgers' equation, AIAA Paper No. 90-1445, AIAA 21st Fluid Dynamics, Plasma Dynamics and Lasers Conference, June 18–20, 1990/Seattle, Washington.
Yee, H. C. (1987). Construction of explicit and implicit symmetric TVD schemes and their application,J. Comput. Phys. 68, 151–179.
Yee, H. C. (1989). Lecture notes on a class of high-resolution explicit and implicit shock-capturing methods, Von Karman Institute for Fluid Dynamics Lecture Series 1989–04. March 6–10, 1989 Rhode-St-Genese, Belgium; also Lecture Notes of Workshop in IAA, Tainan, Taiwan, Nov. 14–15, 1989.
Yee, H. C., Warming, R. F., and Harten, A. (1985). Implicit total variation diminishing (TVD) schemes for steady state calculation,J. Comput. Phys. 57, 327–360.
Zalesak, S. T. (1987). A preliminary comparison of modern shock-capturing schemes: Linear advection,Advances in Computational Methods for Partial Differential Equations, Vol. VI, Vichnevetsky, R., and Stepleman, R. S. (eds.), Publ. IMACS, pp. 15–22.