Abstract
A comparative study is made of three finite volume formulations to investigate the efficacy of flux limiters and damping coefficients on three-dimensional Euler and Navier-Stokes solutions. Spatial discretizations of convective and diffusive fluxes based on a central, a modified central and an upwind schemes are described. The system of ordinary equations is then solved by a factored implicit stepping technique for the computation of supersonic flow over a blunt delta wing. The modified central method, stabilized by flux limiters and a second-order damping, provides high-resolution, non-oscillatory shocks comparable to the characteristic-damped upwind method. It also yields as accurate solutions for viscous flows as the central scheme blended with second- and fourth-order damping.
Similar content being viewed by others
References
Beam, R. M.; Warming, R. F. (1978): An implicit factored scheme for the compressible Navier-Stokes equations. AIAA J. 16, 393–402
Briley, W. R.; McDonald, H. (1976): Solution of the three-dimensional Navier-Stokes equations by an implicit technique. Lecture Notes in Physics, Vol. 35, Berlin, Heidelberg New York: Springer
Desideri, J.-A.; Glowinski, R.; Periaux, J. (1992): Hypersonic flows for reentry problems. Ed. Vol. III, Berlin, Heidelberg, New York: Springer
Eliasson, P.; Rizzi, A.; Srinivasan, S. (1992): Hypersonic leeside delta-wing flow computation using centered schemes. Ed. Vol. II, pp. 981–1005, Berlin, Heidelberg, New York: Springer
Hitzel, S. M. (1992). Inviscid hypersonic flow over a delta wing. Vol. II, pp. 960–980. Berlin, Heidelberg, New York: Springer
Jameson, A. (1985). Numerical solution of the Euler equation for compressible inviscid fluids. In: Angrand, F., et al. (ed.): Numerical Methods for the Euler Equations of Fluid Dynamics. SIAM, Philadelphia 199–231
Li, C. P. (1991): Computational methods for shock waves in three-dimensional supersonic flow. Comput. Meth. Appl. Mech. Eng. 87, 307–327
Li, C. P.; Ma, E. (1992): Delta wing flowfield computations by upwind and centered TVD techniques. Ed. Vol III. Berlin, Heidelberg, New York: Springer
Manna, M.; Deconinck, H.; Ma, E.; Li, C. P. (1992): Validation of high resolution upwind solvers on 3D inviscid hypersonic flow around delta wings. Symposium on Theoretical and Experimental Methods in Hypersonic Flows. AGARD 70th Fluid Dynamics Panel Meeting, Torino, Italy, May
Roe, P. L. (1981): Approximate Riemann solvers, parameter vectors, and difference schemes. J. Comp. Phys. 43, 357–372
Sanders, R.; Li, C. (1992). A variation nonexpansive central differencing scheme for nonlinear hyperbolic conservation laws. Proc. Tenth Inter. Conf. Computing Methods in Applied Sciences and Engineering. Versailles, France, 511–526.
Van Leer, B. (1977): Towards the ultimate conservative difference scheme, part IV. J. Comp. Phys. 23, 276–299
Yee, H. (1986): Linearized form of implicit TVD schemes for multidimensional Euler and Navier-Stokes equations. Comput. Math. Appl. 12A, 413–432
Author information
Authors and Affiliations
Additional information
Communicated by T.E. Tezduyar, July 10, 1992
Rights and permissions
About this article
Cite this article
Li, C.P. Implicit finite volume methods and application to a delta wing problem. Computational Mechanics 11, 408–420 (1993). https://doi.org/10.1007/BF00350096
Issue Date:
DOI: https://doi.org/10.1007/BF00350096