Cost-effective Multiresolution schemes for Shock Computations

Harten's Multiresolution framework has provided a fruitful environment for the development of adaptive codes for hyperbolic PDEs. The so-called cost-effective alternative [4,8,21] seeks to achieve savings in the computational cost of the underlying numerical technique, but not in the overall memory requirements of the code. Since the data structure of the basic algorithm does not need to be modified, it provides a set of tools that can be easily implemented into existing codes and that can be very useful in order to speed up the numerical simulations involved in the testing process that is associated to the development of new numerical schemes. In this paper we present two different applications of the cost-effective multilevel technique developed in [8] in non-standard situations. In both cases, its use has led to a drastic reduction in the computational time required for 2D numerical simulations, and hence to the ability to perform fine mesh simulation and, hence, to investigate new numerical techniques on personal computers