In this expository talk, an overview of approaches for obtaining approximate solutions to the Riemann problem for hyperbolic conservation laws will be presented. We will begin with a brief review of how solutions are constructed analytically, then proceed to discuss approaches to approximate solutions. We will give a high-level overview of the solvers developed by Collela and Glaz, the Roe solver, as well as the HLL/HLLC solvers. If time permits we will discuss the Random Choice Methods and first-order Godunov schemes. Taken as a whole, the goal of this talk is to give a one hour `crash course' in the fundamentals of finite volume schemes for graduate students.

Speaker(s): Jack Wakefield (University of Michigan)