Construction of the Exact Solution of Ripa Model with Primitive Variable Approach

The exact solution of the Riemann problem associated to Ripa model is constructed. A primitive variable formulation of the model is used instead of conserved variable formulation. This lead to establish the solutions to Riemann problem without calculating the flux terms. The closed form solution is obtained in the case of all rarefaction wave. The phase plane curves and corresponding characteristics curves have been plotted for different cases including rarefaction waves and shock waves connecting left and right known states. Many numerical methods for solving nonlinear hyperbolic conservation laws are based on conserved variable formulation, hence the conversion from primitive to conserved variables is required within algorithm. This method gives direct calculation of the exact solution in primitive variable formulation of the model. This method can be effectively applied to design more robust numerical solvers for hyperbolic conservation laws.