General m × m triangular systems of conservation laws in one space dimension are considered. These systems arise in applications like multi-phase flows in porous media and are non-strictly hyperbolic. Simple and efficient finite-volume schemes of the Godunov type are devised. These are based on a local decoupling of the system into a series of single conservation laws with discontinuous coefficients and are hence termed semi-Godunov schemes. These schemes are not based on the characteristic structure of the system. Some useful properties of the schemes are derived and several numerical experiments demonstrate their robustness and computational efficiency.
Discontinuous flux Flows in porous media Godunov type schemes Triangular systems
This is a preview of subscription content, log in to check access.
Karlsen KH, Risebro NH and Towers JD (2003). Upwind difference approximations for degenerate parabolic convection–diffusion equations with a discontinuous coefficient. IMA J Numer Anal 22(4): 623–664
Karlsen KH, Risebro NH and Towers JD (2003). L1 stability for entropy solution of nonlinear degenerate parabolic convection–diffusion equations with discontinuous coefficients. Skr K Nor Vidensk Selsk 3: 49
Adimurthi JJ and Veerappa Gowda GD (2004). Godunov-type methods for conservation laws with a flux function discontinuous in space. SIAM J Numer Anal 42(1): 179–208
Adimurthi J, Mishra S and Veerappa Gowda GD (2005). Optimal entropy solutions for conservation laws with discontinuous flux. Hyp Diff Eqns 2(4): 1–56
Mishra S (2005) Analysis and Numerical approximation of conservation laws with discontinuous coefficients. PhD Thesis, Indian Institute of Science. BangaloreGoogle Scholar
Karlsen KH, Mishra S, Risebro NH (2006) Convergence of finite volume schemes for a triangular system of conservation laws. Preprint.Google Scholar
Chavent G and Jaffre J (1986). Mathematical models and Finite elements for reservoir simulation. North Holland, Amsterdam
Bürger R, Karlsen KH, Tory EM and Wendland WL (2002). Model equations and instability regions for the sedimentation of polydisperse suspensions of spheres. ZAMM Z Angew Math Mech 82(10): 699–722
Karlsen KH, Lie K-A, Natvig JR, Nordhaug HF and Dahle HK (2001). Operator splitting methods for systems of convection-diffusion equations: nonlinear error mechanisms and correction strategies. J Comput Phys 173(2): 636–663