 Generally speaking, Riemann solvers are specific methods for computing the numerical flux across a discontinuity in the Riemann problem.They form an important part of high-resolution schemes; typically the right and left states for the Riemann problem are calculated using some form of nonlinear reconstruction, such as a flux limiter or a WENO method, and then used as the input for the Riemann solver.Sergei K. Godunov is credited with introducing the first exact Riemann solver for the Euler equations, by extending the previous CIR (Courant-Isaacson-Rees) method to non-linear systems of hyperbolic conservation laws.