Falle and Komissarov  have considered two different algorithms to solve the local Riemann problems in SRHD by extending the methods devised in . In a first algorithm, the intermediate states of the Riemann problem at both sides of the contact discontinuity, and , are obtained by solving the system
In the second algorithm proposed by Falle and Komissarov , a linearization of system (41) is obtained by constructing a constant matrix . The solution of the corresponding Riemann problem is that of a linear system with matrix , i.e.,p runs from 1 to the number of equations of the system).
In both algorithms, the final step involves the computation of the numerical fluxes for the conservation equations,
© Max Planck Society and the author(s)