AUSM-Based High-Order Solution for Euler Equations

In this paper we demonstrate the accuracy and robustness of combining the advection upwind splitting method(AUSM),specifically AUSM+-UP[9],with highorder upwind-biased interpolation procedures,theweighted essentially non-oscillatory(WENO-JS)scheme[8]and its variations[2,7],and the monotonicity preserving(MP)scheme[16],for solving the Euler equations.MP is found to be more effective than the three WENO variations studied.AUSM+-UP is also shown to be free of the so-called“carbuncle”phenomenon with the high-order interpolation.The characteristic variables are preferred for interpolation after comparing the results using primitive and conservative variables,even though they require additional matrix-vector operations.Results using the Roe flux with an entropy fix and the Lax-Friedrichs approximate Riemann solvers are also included for comparison.In addition,four reflective boundary condition implementations are compared for their effects on residual convergence and solution accuracy.Finally,a measure for quantifying the efficiency of obtaining high order solutions is proposed;the measure reveals that a maximum return is reached after which no improvement in accuracy is possible for a given grid size.

Extension and Comparative Study of AUSM-Family Schemes for Compressible Multiphase Flow Simulations

Several recently developed AUSM-family numerical flux functions(SLAU,SLAU2,AUSM+-up2,and AUSMPW+)have been successfully extended to compute compressible multiphase flows,based on the stratified flow model concept,by following two previous works:one by M.-S.Liou,C.-H.Chang,L.Nguyen,and T.G.Theofanous[AIAA J.46:2345-2356,2008],in which AUSM+-up was used entirely,and the other by C.-H.Chang,and M.-S.Liou[J.Comput.Phys.225:840-873,2007],in which the exact Riemann solver was combined into AUSM+-up at the phase interface.Through an extensive survey by comparing flux functions,the following are found:(1)AUSM+-up with dissipation parameters of Kp and Ku equal to 0.5 or greater,AUSMPW+,SLAU2,AUSM+-up2,and SLAU can be used to solve benchmark problems,including a shock/water-droplet interaction;(2)SLAU shows oscillatory behaviors[though not as catastrophic as those of AUSM+(a special case of AUSM+-up with Kp=Ku=0)]due to insufficient dissipation arising from its ideal-gas-based dissipation term;and(3)when combined with the exact Riemann solver,AUSM+-up(Kp=Ku=1),SLAU2,and AUSMPW+are applicable to more challenging problems with high pressure ratios.