By Mars Fontana
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The fact that slope-limiting is indispensable has already been demonstrated in the scalar case above. In practice, each of the three basic flow variables is subjected to the same simple algorithm used in the scalar case. 9. Fluid Dynamical Examples Various studies on shock wave phenomena have been conducted in the course of implementing the GRP scheme to the fluid dynamical equations, some of them induding comparison to experiments involving complex wave interactions. Here we consider specifically the four cases: • A rarefaction wave propagating into a narrower duct via a converging nozzle.
O. FRIEDRICHS, Supersonic Flow and Shock Waves. Springer, New York, 1976. J. FALCOVITZ, G. ALFANDARY, AND G. BEN-DoR, Numerical simulation of the head-on reflection of a regular reflection, International Journal for NumerM. BEN-ARTZI, 48 ical Methods in Fluids, 17:1055-1077, 1993. 8. J. GLIMM, G. MARSHALL, AND B. PLOHR , A generalized Riemann problem for quasi one-dimensional gas flows, Adv. App!. , 5:1-30, 1984. 9. E. -A. RAVIART, Hyperbolic Systems of Conservation Laws, Ellipses, 1991. 10. E.
The "acoustic case" VL=VR , V£ f. V~ . as "sound waves", justifying the terminology "acoustic case" used here. 25 Their slopes are -A(O)gL= - A(O)PLCL (for C_) and A(O)gR=A(O)PRCR (for C+), where CL , CR are the initial speeds of sound (in the Eulerian frame), as r -+ 0-, 0+ respectively. When viewed from the side of the contact discontinuity, these slopes are, respectively, -A(O)g; and A(O)g~. Of course, these values are equal to the previous ones, since V* = VL = YR. However, we retain the two-sided notation (like gL, g;, gR' g~ which are all equal) in the formulas.
Corrosion Engineering (Mcgraw-Hill International Editions) by Mars Fontana