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

2014 ◽  
Vol 16 (3) ◽  
pp. 632-674 ◽  
Author(s):  
Keiichi Kitamura ◽  
Meng-Sing Liou ◽  
Chih-Hao Chang
Keyword(s):  
Phase Interface ◽  
Ideal Gas ◽  
Benchmark Problems ◽  
Riemann Solver ◽  
Model Concept ◽  
Flow Simulations ◽  
Dissipation Term ◽  
Compressible Multiphase Flow ◽  
Exact Riemann Solver ◽  
Special Case

AbstractSeveral recently developed AUSM-family numerical flux functions (SLAU, SLAU2, AUSMM+-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.

The development of a Riemann solver for the steady supersonic Euler equations

1994 ◽  
Vol 98 (979) ◽  
pp. 325-339 ◽  
Author(s):  
E. F. Toro ◽  
A. Chakraborty
Keyword(s):  
Euler Equations ◽  
Weighted Average ◽  
Godunov Method ◽  
Riemann Solver ◽  
Flux Method ◽  
First Order ◽  
Enhanced Resolution ◽  
Average Flux ◽  
Exact Riemann Solver ◽  
Order Weighted Average

Abstract An improved version (HLLC) of the Harten, Lax, van Leer Riemann solver (HLL) for the steady supersonic Euler equations is presented. Unlike the HLL, the HLLC version admits the presence of the slip line in the structure of the solution. This leads to enhanced resolution of computed slip lines by Godunov type methods. We assess the HLLC solver in the context of the first order Godunov method and the second order weighted average flux method (WAF). It is shown that the improvement embodied in the HLLC solver over the HLL solver is virtually equivalent to incorporating the exact Riemann solver.

scholarly journals Collapsing Cavities and Converging Shocks in Non-Ideal Materials

2019 ◽  
Vol 72 (4) ◽  
pp. 501-520 ◽  
Author(s):  
Zachary M Boyd ◽  
Emma M Schmidt ◽  
Scott D Ramsey ◽  
Roy S Baty
Keyword(s):  
Gas Dynamics ◽  
Nonlinear Eigenvalue Problem ◽  
Ideal Gas ◽  
Test Problems ◽  
Infinite Dimensional ◽  
Cavity Collapse ◽  
Scaling Solution ◽  
Metal Deformation ◽  
Special Case ◽  
The Ideal

Summary As modern hydrodynamic codes increase in sophistication, the availability of realistic test problems becomes increasingly important. In gas dynamics, one common unrealistic aspect of most test problems is the ideal gas assumption, which is unsuited to many real applications, especially those involving high pressure and speed metal deformation. Our work considers the collapsing cavity and converging shock test problems, showing to what extent the ideal gas assumption can be removed from their specification. It is found that while most materials simply do not admit simple (that is scaling) solutions in this context, there are infinite-dimensional families of materials which do admit such solutions. We characterize such materials, derive the appropriate ordinary differential equations and analyze the associated nonlinear eigenvalue problem. It is shown that there is an inherent tension between boundedness of the solution, boundedness of its derivatives and the entropy condition. The special case of a constant-speed cavity collapse is considered and found to be heuristically possible, contrary to common intuition. Finally, we give an example of a concrete non-ideal collapsing cavity scaling solution based on a recently proposed pseudo-Mie–Gruneisen equation of state.

scholarly journals An improved exact Riemann solver for relativistic hydrodynamics

2001 ◽  
Vol 449 ◽  
pp. 395-411 ◽  
Author(s):  
LUCIANO REZZOLLA ◽  
OLINDO ZANOTTI
Keyword(s):  
Riemann Problem ◽  
Initial Conditions ◽  
Wave Pattern ◽  
Initial Guess ◽  
Relativistic Velocity ◽  
Riemann Solver ◽  
Rarefaction Waves ◽  
Riemann Solvers ◽  
Velocity Jump ◽  
Exact Riemann Solver

A Riemann problem with prescribed initial conditions will produce one of three possible wave patterns corresponding to the propagation of the different discontinuities that will be produced once the system is allowed to relax. In general, when solving the Riemann problem numerically, the determination of the specific wave pattern produced is obtained through some initial guess which can be successively discarded or improved. We here discuss a new procedure, suitable for implementation in an exact Riemann solver in one dimension, which removes the initial ambiguity in the wave pattern. In particular we focus our attention on the relativistic velocity jump between the two initial states and use this to determine, through some analytic conditions, the wave pattern produced by the decay of the initial discontinuity. The exact Riemann problem is then solved by means of calculating the root of a nonlinear equation. Interestingly, in the case of two rarefaction waves, this root can even be found analytically. Our procedure is straightforward to implement numerically and improves the efficiency of numerical codes based on exact Riemann solvers.

scholarly journals PHASE SPACE MEASURE CONCENTRATION FOR AN IDEAL GAS

2009 ◽  
Vol 23 (08) ◽  
pp. 1013-1025 ◽  
Author(s):  
ANTHONY J. CREACO ◽  
NIKOS KALOGEROPOULOS
Keyword(s):  
Phase Space ◽  
Isoperimetric Inequality ◽  
Thermodynamic Limit ◽  
Ideal Gas ◽  
Measure Concentration ◽  
Special Case

We point out that a special case of an ideal gas exhibits concentration of the volume of its phase space, which is a sphere, around its equator in the thermodynamic limit. The rate of approach to the thermodynamic limit is determined. Our argument relies on the spherical isoperimetric inequality of Lévy and Gromov.

scholarly journals An Exact Riemann Solver for Multicomponent Turbulent Flow

2000 ◽  
Vol 14 (2) ◽  
pp. 117-131 ◽  
Author(s):  
EMMANUELLE DECLERCQ ◽  
ALAIN FORESTIER ◽  
JEAN-MARC HÉRARD ◽  
XAVIER LOUIS ◽  
GÉRARD POISSANT
Keyword(s):  
Turbulent Flow ◽  
Riemann Solver ◽  
Exact Riemann Solver

Compressible Subsonic Flow in Two-dimensional Channels

1955 ◽  
Vol 6 (3) ◽  
pp. 205-220 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Conformal Mapping ◽  
Direct Problem ◽  
Subsonic Flow ◽  
Ideal Gas ◽  
Inviscid Fluid ◽  
Two Dimensional ◽  
Step Functions ◽  
Curved Walls ◽  
Special Case ◽  
The Ideal

SummaryEquations for the calculation of the subsonic flow of an inviscid fluid through given two-dimensional channels (the “ direct” problem), and for the design (the “ indirect” problem) of such channels are derived. The method is based on conformal mapping, and in the special case of channels with walls made from a number of straight sections, or with wall pressure prescribed as step-functions, yields the same results as the well-known Schwarz-Christoffel mapping theorem technique. However, it is more general than this latter method, since it is capable of dealing with curved walls or continuously varying wall pressures. The compressibility of the fluid is allowed for only approximately, the ideal gas being replaced by a Kàrmàn-Tsien tangent gas.In Part II the theory is applied to various problems of aeronautical interest, perhaps the most important of which is to the setting of “ streamlined ” walls about a symmetrical aerofoil placed in the centre of the channel.

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