Artificial boundary conditions for the Burgers equation on the plane

The numerical solution of the initial value problem for the two-dimensional Burgers equa- tion on the whole plane is considered. Usual techniques, like finite difference methods and finite element methods cannot be directly applied for the solution of this problem, because the corresponding domain is unbounded. We propose a new method to overcome this dif- ficulty. The efficiency of the proposed method is tested by several numerical examples.