Upwind finite volume solution of sensitivity equations for hyperbolic systems of conservation laws with discontinuous solutions

Computers and Fluids

Volumn 38, Issue 9, 2009, Pages 1697-1709

  Guinot, V ^a  

^a UNIVERSITÉ DE MONTPELLIER   (France)

Author keywords

[No Author keywords available]

Indexed keywords

ANALYTICAL SOLUTIONS; DIRECT SOLUTION; DISCONTINUOUS SOLUTIONS; FINITE VOLUME SOLUTION; HYPERBOLIC SYSTEM; HYPERBOLIC SYSTEMS OF CONSERVATION LAWS; RIEMANN SOLVER; SAINT VENANT EQUATION; SCALAR ADVECTION; SENSITIVITY EQUATIONS; SENSITIVITY VECTORS; SOURCE TERMS; THIRD COMPONENT;

EID: 67650436066     PISSN: 00457930     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.compfluid.2009.03.002     Document Type: Article

References (30)

1. Anderson M.L., Bangerth W., and Carey G.F. Analysis of parameter sensitivity and experimental design for a class of nonlinear partial differential equations. International Journal for Numerical Methods in Fluids 48 (2005) 583-605
2. Atkinson A.C., and Donev A.N. Optimum experimental design (1992), Clarendon Press, Oxford
3. Bardos C., and Pironneau O. A formalism for the differentiation of conservation laws. Comp R Acad Sci I335 (2002) 839-845
4. 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
5. Davis S.F. Simplified second-order Godunov-type methods. SIAM J Sci Statist Comput 9 (1988) 445-473
6. Dressler R.F. Unsteady non-linear waves in sloping channels. Proc Roy Soc London Ser A 247 (1958) 186-198
7. Godunov S.K. A difference method for the calculation of discontinuous solutions of hydrodynamics. Mat Sb 47 (1959) 271-300
8. Griewank A. Evaluating derivatives: principles and techniques of algorithmic differentiation (2000), SIAM, Philadelphia (PA)
9. Guinot V, Cappelaere B. Sensitivity equations for the 1D shallow water equations. Practical application to model calibration. J Hydrol Eng [to appear].
10. Guinot V., and Cappelaere B. Sensitivity analysis of 2D steady-state shallow water flow. Application to free surface flow model calibration. Adv Water Resour 32 4 (2009) 540-560
11. Guinot V., Delenne C., and Cappelaere B. An approximate Riemann solver for sensitivity equations with discontinuous solutions. Adv Water Resour 32 1 (2009) 61-77
12. Guinot V., Leménager M., and Cappelaere B. Sensitivity equations for hyperbolic conservation law-based flow models. Adv Water Resour 30 (2007) 1943-1961
13. Gunzburger M.D. Sensitivities, adjoints and flow optimization problems. Int J Numer Meth Fluids 31 (1999) 53-78
14. 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
15. Kleiber M., Antunez H., Hien T.D., and Kowalczyk P. Parameter Sensitivity in nonlinear mechanics (1997), Wiley, New York
16. Li B., and Yeh T.C.J. Sensitivity and moment analyses of head in variably saturated regimes. Adv Water Resour 21 (1998) 477-485
17. Lu S., and Sagaut P. Direct sensitivity analysis for smooth unsteady compressible flow using complex differentiation. Int J Numer Meth Fluids 53 12 (2007) 1863-1886
18. Lyness J.N., and Moler C.B. Numerical differentiation of analytic functions. SIAM J Numer Anal 4 2 (1967) 202-210
19. Maskey S., and Guinot V. Improved first-order second moment method for uncertainty estimation in flood forecasting. Hydrol Sci J 48 (2003) 183-196
20. Nujic M. Efficient implementation of nonoscillatory schemes for the computation of free-surface flows. J Hydraul Res 33 (1995) 101-111
21. Papadimitriou D.I., and Giannkoglou K.C. Direct, adjoint and miwed approaches for the computation of Hessian in airfoil design problems. Int J Numer Meth Fluids 56 (2008) 1929-1943
22. Piasecki M., and Katopodes N.D. Control of contaminant releases in rivers I: adjoint sensitivity analysis. J Hydraul Eng 123 6 (1997) 486-492
23. Pironneau O. On optimum design in fluid mechanics. J Fluid Mech 64 (1974) 97-110
24. Saltelli A. What is sensitivity analysis? In: Saltelli A, Chan K, Scott EM, editors. Sensitivity analysis. Wiley series in probability and statistics; 2000. p. 3-13.
25. Sanders B.F., and Katopodes N.D. Control of canal flow by adjoint sensitivity method. J Irrig Drain Eng 125 5 (1999) 287-297
26. Stoker J.J. Water waves (1957), Interscience, New York
27. Toro E.F., Spruce M., and Speares W. Restoration of the contact surface in the HLL-Riemann solver. Shock Waves 4 (1994) 25-34
28. Turànyi T, Rabitz H. Local methods. In: Saltelli A, Chan K, Scott EM, editors. Sensitivity analysis. Wiley series in probability and statistics; 2000. p. 81-99.
29. 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
30. White L.W., Vieux B., Armand D., and LeDimet F.X. Astimation of optimal parameters for a surface hydrology model. Adv Water Resour 26 (2003) 337-348