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Stable numerical methods for conservation laws with discontinuous flux function. (English) Zbl 1088.65080
Summary: We develop numerical methods for solving nonlinear equations of conservation laws with flux function that depends on discontinuous coefficients. Using a relaxation approximation, the nonlinear equation is transformed to a semilinear diagonalizable problem with linear characteristic variables. Eulerian and Lagrangian methods are used for the advection stage while an implicit-explicit scheme solves the relaxation stage. The main advantages of this approach are neither Riemann problem solvers nor linear iterations are required during the solution process. Moreover, the characteristic-based relaxation method is unconditionally stable such that no CFL conditions are imposed on the selection of time steps. Numerical results are shown for models on traffic flows and two-phase flows.

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35L65 Hyperbolic conservation laws
90B20 Traffic problems in operations research
76T10 Liquid-gas two-phase flows, bubbly flows
65M25 Numerical aspects of the method of characteristics for initial value and initial-boundary value problems involving PDEs
Full Text: DOI
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