A Block Structured Adaptive Solution to the Shallow Water Equations

An adaptive mesh refinement algorithm for shallow water equations is presented. The algorithm uses upwind scheme that is Godunov type and which approximately solves the Riemann problem using Roe\u27s technique. A highly accurate solution is achieved by using the adaptive mesh refinement technique of Berger and Oliger for mesh refinement algorithm. The numerical method is second-order accurate and approximately max-min preserving by using van Leer limited-slope technique. One-dimensional nesting algorithm has been implemented successfully. Numerical results on a test problem verify the second order accuracy of the algorithm. The nested grid results yield the equivalent solution to that of the corresponding fine grid solution