A priori reduction method for solving the two-dimensional Burgers’ equations

摘要

The two-dimensional Burgers’ equations are solved here using the A Priori Reduction method. This method is based on an iterative procedure which consists in building a basis for the solution where at each iteration the basis is improved. The method is called a priori because it does not need any prior knowledge of the solution, which is not the case if the standard Karhunen–Loéve decomposition is used. The accuracy of the APR method is compared with the standard Newton–Raphson scheme and with results from the literature. The APR basis is also compared with the Karhunen–Loéve basis.