Parallel Hopscotch Method for Shallow Water Equations 1 Shallow Water Model

Shallow water equations arise in many scientiic applications, for example climate modeling. The numerical solution of such equations requires a very large amount of computation which is suitable for parallelization. The odd-even Hopscotch method is parallelizable and is applied to solve this problem. Our aim is to investigate the performance of the method implemented on the virtual shared memory Kendall Square Research (KSR1) machine. The primitive equations describing incompressible inviscid ow with a free surface are called the shallow water equations. In two space dimensions the equations are of the form @u @t + u @u @x + v @u @y + g @h @x ? fv = 0 @v @t + u @v @x + v @v @y + g @h @y + fu = 0 @h @t + @(hu) @x + @(hv) @y = 0 where u; v are the velocity components in x? and y?directions respectively, h is the height of water surface, g is gravitational acceleration (assumed constant) and f = f 0 + (y ? Y=2) (f 0 ; constants) is the Coriolis parameter. If we introduce the vector w = u; v; h] T then the above system of equations may be represented as @w @t + A(w) @w @x + B(w) @w @y + Cw = 0 (1) where A(w) = 2 6 4