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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
    Restoration of the contact surface in the HLL-Riemann solver (1994)
    Springer
    Shock waves 4 (1994), S. 25-34 
    Details
    ISSN: 1432-2153
    Keywords: Finite difference scheme ; Numerical simulation ; Riemann solver
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics , Technology
    Notes: Abstract The missing contact surface in the approximate Riemann solver of Harten, Lax, and van Leer is restored. This is achieved following the same principles as in the original solver. We also present new ways of obtaining wave-speed estimates. The resulting solver is as accurate and robust as the exact Riemann solver, but it is simpler and computationally more efficient than the latter, particulaly for non-ideal gases. The improved Riemann solver is implemented in the second-order WAF method and tested for one-dimensional problems with exact solutions and for a two-dimensional problem with experimental results.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01414629
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  • 3
    Electronic Resource
    Electronic Resource
    Types of stationary points in a variational formulation of shallow-water flows (1984)
    Springer
    Journal of engineering mathematics 18 (1984), S. 195-205 
    Details
    ISSN: 1573-2703
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Technology
    Notes: Summary Free-surface gravity flows are stationary points of a functional J when the problem is formulated variationally. Here we are concerned with the problem of determining the nature of the stationary point, that is, whether it is a minimum, a maximum, a saddle point or whether a singularity occurs. This is a problem of both theoretical and computational importance. Within a variational approximation of shallow-water type developed by the authors, we prove some new results on the problem. The analysis is carried out by studying the second variation of the functional J and the corresponding Jacobi's equation. Reference is also made to numerical experiments which confirm the findings. The experiments also suggest that such findings may well extend to flows outside the class of shallow-water flows governed by the model used in the analysis.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00039188
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  • 4
    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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  • 5
    Electronic Resource
    Electronic Resource
    Mesh effects on the computation of small amplitude water waves (1985)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 5 (1985), S. 505-513 
    Details
    ISSN: 0271-2091
    Keywords: 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: Computational difficulties arise in the non-linear free-surface problem for water waves both at large amplitudes when the crest becomes nearly singular and at small amplitudes when the wave is very close to the alternative uniform flow solution. Since the limiting wavelengths for small amplitude waves are known from the Stokes linearized theory, these are used in checking results for finite-amplitude programs. When Southwell and Vaisey1 first tried this, their methods gave an unexplained overestimate, by 6 per cent, of the limiting wavelength. This paper shows how coarse mesh effects can create such an overestimate, gives very accurate solutions at small amplitudes and considers accuracy in relation to the mesh for short and long waves.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650050602
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  • 6
    Electronic Resource
    Electronic Resource
    Transition bifurcation branches in non-linear water waves (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 219-227 
    Details
    ISSN: 0271-2091
    Keywords: Water Waves ; Bifurcation ; Non-linear ; 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: We are concerned with the numerical computation of progressive free surface gravity waves on a horizontal bed. They are regarded as families of bifurcation branches (λ,A)Q of constant discharge Q.Numerically we determine two transition values Q1 and Q2 with corresponding transition bifurcation branches that classify waves into three disjoint branch sets B1, B2 and B3. Their members are families of waves (λ,A)Q satisfying the conditions 0〈Q2 ≤Q12, Q12 〈Q2 ≤Q22 and Q22 〈Q2 〈B/27, respectively.The bifurcation patterns are analysed in some detail from the computed bifurcation diagram, which shows that in B1 bifurcation is to the left and the amplitude A increases as the wavelength λ decreases; in B2 bifurcation is to the right and turning points are observed nearly at breaking point. In B3 bifurcation is to the right and A increases monotonically with λ.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650060404
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  • 7
    Electronic Resource
    Electronic Resource
    Mesh effects on the computation of non-linear gravity waves of arbitrary discharge (1986)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 6 (1986), S. 479-493 
    Details
    ISSN: 0271-2091
    Keywords: Gravity Waves ; Kantorovich Method ; Mesh Effects ; 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: Numerical computations of non-linear gravity waves are presented and the effects of mesh variations on the results are discussed.Waves are regarded as two-parameter families (λ,A)Q of arbitrary discharge Q, and computations are carried out using a new Kantorovich algorithm.Mesh effects are to a large extent dependent on the particular wave region under consideration. Three such regions are identified and typical examples are computed and discussed.
    Additional Material: 8 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650060706
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  • 8
    Electronic Resource
    Electronic Resource
    Numerical computations of critical flow over a weir (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 499-509 
    Details
    ISSN: 0271-2091
    Keywords: Critical Flow Rate ; Finite Elements ; Free Surface ; Weir ; 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: Computing critical flows in hydraulics involves three problems in one: the internal flow problem, the location of the free surface and the determination of the critical flow rate. The subject can involve such difficulties as non-uniqueness, non-existence, ill-conditioning and catastrophes.This paper discusses the difficulties relating to computing critical flows over weirs. A new rapidly convergent method of determining the critical flow rate is presented and various results are shown using it with finite element discretization and with a new streamline shifting method. Numerical results are in good agreement with published data, both numerical and experimental.
    Additional Material: 6 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650040604
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  • 9
    Electronic Resource
    Electronic Resource
    A Kantorovich computational method for free surface gravity flows (1984)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 4 (1984), S. 1137-1148 
    Details
    ISSN: 0271-2091
    Keywords: Free Surface Flows ; Computation ; Kantorovich Method ; 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: Computing free surface gravity flows involves basically two coupled problems, namely, the location of the free surface position and the determination of the internal flow field (for assumed values H0 and Q of the total head and discharge, respectively).Solution techniques are invariably based on iterative procedures, but those that iterate between the two coupled problems may become unstable.In this paper we present a computational method in which the coupling is kept throughout the process of iteration. This is achieved by converting the coupled problems (by means of the Kantorovich method) into the single problem of finding a set of streamlines, including that of the free surface. These streamlines are moved (iteratively) to satisfy the stationary conditions of the governing variational principle.The algorithm is very stable and converges rapidly. It is also easy to implement to solve various types of steady flows with a free surface under gravity.
    Additional Material: 5 Ill.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1002/fld.1650041204
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    Paper (German National Licenses)
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  • 10
    Electronic Resource
    Electronic Resource
    On Riemann solvers for compressible liquids (1998)
    Chichester : Wiley-Blackwell
    International Journal for Numerical Methods in Fluids 28 (1998), S. 395-418 
    Details
    ISSN: 0271-2091
    Keywords: compressible liquid ; Riemann solvers ; approximate Riemann solvers ; Tammann equation of state ; Tait equation of state ; Engineering ; Numerical Methods and Modeling
    Source: Wiley InterScience Backfile Collection 1832-2000
    Topics: Mechanical Engineering, Materials Science, Production Engineering, Mining and Metallurgy, Traffic Engineering, Precision Mechanics
    Notes: A number of Riemann solvers are proposed for the solution of the Riemann problem in a compressible liquid. Both the Tait and Tammann equations of state are used to describe the liquid. Along with exact Riemann solvers, a detailed description of a primitive variable Riemann solver, a two-shock Riemann solver, a two-rarefaction Riemann solver and an extension to the HLL Riemann solver, namely the HLLC Riemann solver, are presented. It is shown how these Riemann solvers may be implemented into Godunov-type numerical methods. The appropriateness of each of the Riemann solvers for a number of flow situations is demonstrated by applying Godunov's method to some revealing shock tube test problems. © 1998 John Wiley & Sons, Ltd.
    Additional Material: 7 Ill.
    Type of Medium: Electronic Resource
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