engleski

Godunov Scheme for the Scalar Nonlinear Conservation Laws with Flux Depending on the Space Variable

We derive the Godunov scheme for the scalar nonlinear conservation laws with the flux depending on the space variable x and on the unknovn function. The Riemann problem for the scalar conservation law with the flux F(x, u)=k(x)f(u) has been solved and corresponding Godunov scheme is derived. Then we prove that derived scheme has the TVB property. Finally, the numerical examples involving Burger's equation and the Buckley-Leverett equation are presented.

Riemann problem; Flux depending on space variable; Nonlinear conservation laws; Godunov scheme

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