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  • 1
    Electronic Resource
    Electronic Resource
    Direct Riemann solvers for the time-dependent Euler equations (1995)
    Springer
    Shock waves 5 (1995), S. 75-80 
    Details
    ISSN: 1432-2153
    Keywords: Hyperbolic systems ; Riemann problem ; Approximate Riemann solvers ; Godunov-type methods
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics , Technology
    Notes: Abstract Approaches for finding direct, approximate solutions to the Riemann problem are presented. These result in three approximate Riemann solvers. Here we discuss the time-dependent Euler equations but the ideas are applicable to other systems. The approximate solvers are (i) assessed on local Riemann problems with exact solutions and (ii) used in conjunction with the Weighted Average Flux (WAF) method to solve the two-dimensional Euler equations numerically. The resulting numerical technique is assessed on a shock reflection problem. Comparison with experimental observation is carried out.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF02425037
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  • 2
    Electronic Resource
    Electronic Resource
    A fast riemann solver with constant covolume applied to the random choice method (1989)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 9 (1989), S. 1145-1164 
    Details
    ISSN: 0271-2091
    Keywords: Riemann problem ; Covolume ; Random choice ; Engineering ; Engineering General
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: The Riemann problem for the unsteady one-dimensional Euler equations together with the constant-covolume equation of state is solved exactly. The solution is then applied to the random choice method to solve the general initial-boundary value problem for the Euler equations. The iterative procedure to find p*, the pressure between the acoustic waves, involves a single algebraic (non-linear) equation, all other quantities follow directly throughout the x-t plane, except within rarefaction fans where an extra iterative procedure is required. The solution is validated against existing exact results both directly and in conjunction with the random choice method.
    Additional Material: 11 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650090908
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