Department of Mathematics, University of Maryland, College Park
A survey of some of the issues involved in large--scale calculations for systems of conservation laws is given, although we restrict to Godunov--like schemes. The main focus of the talk (and the reason for the word `general' in the title) will be problems for which the solution to the Riemann problem is either unknown or very difficult (equivalent to expensive for the main examples discussed) to obtain approximately. The talk will be INTRODUCTORY throughout.