Methods for Multi–Dimensional PDEs

This chapter is concerned with numerical methods for solving non–linear systems of hyperbolic conservation laws in multidimensions. For Cartesian geometries one may write the equations of our interest here as

$$\mathbf{U}_t+\mathbf{F}(\mathbf{U})_x+\mathbf{G}(\mathbf{U})_y+\mathbf{H}(\mathbf{U})_z=\mathbf{0},$$

((16.1))

where t denotes time or a time–like variable and x, y, z are Cartesian coordinate directions.