Calculation of shocked flows by mathematical programming

A framework for using mathematical programming to solve Burgers' equation is presented. The steady-state inviscid Burgers' equation with given boundary conditions is considered, and the physically relevant solution is discretized using a four-point difference scheme for the viscous term and a two-point difference scheme for the inviscid term. The framework is then used to solve the Euler equations for quasi-one-dimensional flows on grids with variable spacing.