SEVERAL NEW NUMERICAL-METHODS FOR COMPRESSIBLE SHEAR-LAYER SIMULATIONS

被引:365
作者
KENNEDY, CA
CARPENTER, MH
机构
[1] NASA,LANGLEY RES CTR,MS-156,HAMPTON,VA 23681
[2] UNIV CALIF SAN DIEGO,DEPT APPL MECH & ENGN SCI,LA JOLLA,CA 92093
基金
美国国家航空航天局;
关键词
D O I
10.1016/0168-9274(94)00004-2
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
An investigation is conducted of several numerical schemes for use in the computation of two-dimensional, spatially evolving, laminar, variable-density compressible shear layers. Schemes with various temporal accuracies and arbitrary spatial accuracy for both inviscid and viscous terms are presented and analyzed. All integration schemes make use of explicit or compact finite-difference derivative operators. Three classes of schemes are considered: an extension of MacCormack's original second-order temporally accurate method, a new third-order temporally accurate variant of the coupled space-time schemes proposed by Rusanov and by Kutler et al. (RKLW), and third- and fourth-order Runge-Kutta schemes. The RKLW scheme offers the simplicity and robustness of the MacCormack schemes and gives the stability domain and the nonlinear third-order temporal accuracy of the Runge-Kutta method. In each of the schemes, stability and formal accuracy are considered for the interior operators on the convection-diffusion equation U(t) + aU(x) = a(v)U(xx) for which a and alpha(v) are constant. Both spatial and temporal accuracies are verified on the equation U(t) = [b(x)U(x)]x, as well as on U(t) + F(x) = 0. Numerical boundary treatments of various orders of accuracy are chosen and evaluated for asymptotic stability. Formally accurate boundary conditions are derived for explicit sixth-order, pentadiagonal sixth-order, and explicit, tridiagonal, and pentadiagonal eighth-order central-difference operators when used in conjunction with Runge-Kutta integrators. Damping of high wavenumber, nonphysical information is accomplished for all schemes with the use of explicit filters, derived up to sixth order on the boundaries and twelfth order in the interior. Several schemes are used to compute variable-density compressible shear layers, where regions of large gradients of flowfield variables arise near and away from the shear-layer centerline. Results indicate that in the present simulations, the effects of differences in temporal and spatial accuracy between the schemes were less important than the filtering effects. Extended MacCormack schemes were very robust, but were inefficient because of restrictive CFL limits. The third-order temporally accurate RKLW schemes were less dissipative, but had shorter run times. Runge-Kutta integrators did not possess sufficient dissipation to be useful candidates for the computation of variable-density compressible shear layers at the levels of resolution used in the current work.
引用
收藏
页码:397 / 433
页数:37
相关论文
共 65 条
[1]   DIFFERENCE SCHEMES WITH 4TH ORDER ACCURACY FOR HYPERBOLIC EQUATIONS [J].
ABARBANEL, S ;
GOTTLIEB, D ;
TURKEL, E .
SIAM JOURNAL ON APPLIED MATHEMATICS, 1975, 29 (02) :329-351
[2]   SECONDARY FREQUENCIES IN THE WAKE OF A CIRCULAR-CYLINDER WITH VORTEX SHEDDING [J].
ABARBANEL, SS ;
DON, WS ;
GOTTLIEB, D ;
RUDY, DH ;
TOWNSEND, JC .
JOURNAL OF FLUID MECHANICS, 1991, 225 :557-574
[3]  
ANDERSON D, 1974, J ATMOS SCI, V31, P1500, DOI 10.1175/1520-0469(1974)031<1500:ACONSO>2.0.CO
[4]  
2
[5]  
Anderson D. A., 2020, COMPUTATIONAL FLUID, VFourth
[6]  
ANDERSON JM, 1974, ACTA LINGUIST HAF, V15, P1
[7]  
BAYLIS A, 1985, NASA177994 CONTR REP
[8]   ANALYTICAL LINEAR NUMERICAL STABILITY CONDITIONS FOR AN ANISOTROPIC 3-DIMENSIONAL ADVECTION-DIFFUSION EQUATION [J].
BECKERS, JM .
SIAM JOURNAL ON NUMERICAL ANALYSIS, 1992, 29 (03) :701-713
[9]  
Burstein S. Z., 1970, J COMPUT PHYS, V5, P547, DOI [10.1016/0021-9991(70)90080-X, DOI 10.1016/0021-9991(70)90080-X]
[10]   STABLE AND ACCURATE BOUNDARY TREATMENTS FOR COMPACT, HIGH-ORDER FINITE-DIFFERENCE SCHEMES [J].
CARPENTER, MH ;
GOTTLIEB, D ;
ABARBANEL, S .
APPLIED NUMERICAL MATHEMATICS, 1993, 12 (1-3) :55-87