An approximate Riemann solver for sensitivity equations with discontinuous solutions

Advances in Water Resources

Volumn 32, Issue 1, 2009, Pages 61-77

  Guinot, V ^a   Delenne, C ^a   Cappelaere, B ^a  

^a UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

Conservation laws; Hyperbolic systems; Riemann solver; Sensitivity

Indexed keywords

GAS DYNAMICS; HYDRAULIC STRUCTURES; NONLINEAR CONTROL SYSTEMS; TWO DIMENSIONAL;

APPROXIMATE RIEMANN SOLVERS; CONSERVATION LAWS; DIRAC FUNCTIONS; DISCONTINUOUS SOLUTIONS; EMPIRICAL APPROACHES; FLOW PROBLEMS; FREE SURFACE FLOWS; GOVERNING EQUATIONS; HYPERBOLIC SYSTEMS; HYPERBOLIC SYSTEMS OF CONSERVATION LAWS; MODEL OUTPUTS; NUMERICAL SOLUTIONS; PARTIAL DERIVATIVES; RIEMANN SOLVER; SENSITIVITY; SENSITIVITY EQUATIONS; SHALLOW WATER EQUATIONS; SOURCE TERMS; TEST CASES; WITH OR WITHOUT;

EULER EQUATIONS;

EMPIRICAL ANALYSIS; EULER FLOW; FREE SURFACE FLOW; NUMERICAL METHOD; PARAMETERIZATION; SENSITIVITY ANALYSIS; SHALLOW-WATER EQUATION; TWO-DIMENSIONAL FLOW;

EID: 57349194253     PISSN: 03091708     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.advwatres.2008.10.002     Document Type: Article

References (33)

1. Sanders B.F., and Katopodes N.D. Control of canal flow by adjoint sensitivity method. J Irrigat Drain Eng 125 5 (1999) 287-297
2. Piasecki M., and Katopodes N.D. Control of contaminant releases in rivers. I: Adjoint sensitivity analysis. J Hydraul Eng 123 6 (1997) 486-492
3. Papadimitriou D.I., and Giannkoglou K.C. Direct, adjoint and mixed approaches for the computation of Hessian in airfoil design problems. Int J Numer Methods Fluids 56 (2008) 1929-1943
4. Pironneau O. On optimum design in fluid mechanics. J Fluid Mech 64 (1974) 97-110
5. White L.W., Vieux B., Armand D., and LeDimet F.X. Estimation of optimal parameters for a surface hydrology model. Adv Water Res 26 (2003) 337-348
6. Certes C., and de Marsily G. Application of the pilot point method to the identification of aquifer transmisivities. Adv Water Res 14 5 (1991) 284-300
7. Li B., and Yeh T.C.J. Sensitivity and moment analyses of head in variably saturated regimes. Adv Water Res 21 (1998) 477-485
8. Maskey S., and Guinot V. Improved first-order second moment method for uncertainty estimation in flood forecasting. Hydrol Sci J 48 (2003) 183-196
9. Anderson M.L., Bangerth W., and Carey G.F. Analysis of parameter sensitivity and experimental design for a class of nonlinear partial differential equations. Int J Numer Methods Fluids 48 (2005) 583-605
10. Atkinson A.C., and Donev A.N. Optimum experimental design (1992), Clarendon Press, Oxford
11. Griewank A. Evaluating derivatives: principles and techniques of algorithmic differentiation (2000), SIAM, Philadelphia
12. Kleiber M., Antunez H., Hien T.D., and Kowalczyk P. Parameter sensitivity in nonlinear mechanics (1997), Wiley, NY
13. Lu S., and Sagaut P. Direct sensitivity analysis for smooth unsteady compressible flow using complex differentiation. Int J Numer Methods Fluids 53 12 (2007) 1863-1886
14. Lyness J.N., and Moler C.B. Numerical differentiation of analytic functions. SIAM J Numer Anal 4 2 (1967) 202-210
15. Gunzburger M.D. Sensitivities, adjoints and flow optimization problems. Int J Numer Methods Fluids 31 (1999) 53-78
16. Godunov S.K. A difference method for the calculation of discontinuous solutions of hydrodynamics. Matematicheski Sbornik 47 (1959) 271-300
17. Guinot V., Leménager M., and Cappelaere B. Sensitivity equations for hyperbolic conservation law-based flow models. Adv Water Res 30 (2007) 1943-1961
18. Bardos C., and Pironneau O. A formalism for the differentiation of conservation laws. Comptes Rendus de l'Académie des Sci I335 (2002) 839-845
19. Guinot V. Godunov-type schemes. An introduction for engineers (2003), Elsevier
20. Lax P.D. Hyperbolic systems of conservation laws. Commun Pure Appl Math 10 (1957) 537-566
21. Guinot V. Wave propagation in fluids. Models and numerical techniques (2006), Wiley-ISTE
22. Harten A., Lax P.D., and Van Leer B. On upstream differencing and Godunov-type schemes for hyperbolic conservation laws. J Comput Phys 50 (1983) 235-269
23. Davis S.F. Simplified second-order Godunov-type methods. SIAM J Sci Stat Comput 9 (1988) 445-473
24. Toro E.F., Spruce M., and Speares W. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4 (1994) 25-34
25. Toro E.F. Riemann solvers and numerical methods for fluid dynamics (1997), Springer
26. Colella P. Glimm's method for gas dynamics. SIAM J Sci Stat Comput 3 (1976) 76-110
27. Dukowicz J. A general, non-iterative Riemann solver for Godunov's method. J Comput Phys 61 (1985) 119-137
28. Guinot V. Riemann solvers for water hammer simulations by Godunov method. Int J Numer Methods Eng 49 (2000) 851-870
29. Guinot V. Numerical simulation of two-phase flow in pipes using Godunov method. Int J Numer Methods Eng 50 (2001) 1169-1189
30. Lhomme J., and Guinot V. A general, approximate-state Riemann solver for hyperbolic systems of conservation laws with source terms. Int J Numer Methods Fluids 56 9 (2007) 1605-1623
31. Vazquez-Cendon M.E. Improved treatment of source terms in upwind schemes for the shallow water equations in channels with irregular geometry. J Comput Phys 148 2 (1999) 497-526
32. Stoker J.J. Water waves. Interscience (1957)
33. Dressler R.F. Unsteady non-linear waves in sloping channels. Proc Royal Society of London Series A 247 (1958) 186-198