Numerical simulation of the stochastic Burgers’ equation using MLMC and CBC algorithm

Burgers turbulence is a model for developing tools to study the Navier-Stokes turbulence, many hydrodynamical problemsin the theory related to random Lagrangian systems. Many questions that are generally asked in Navier-Stokes turbulence can be answered using Burgers turbulence. The aim of the present paper is to apply Multi-level Monte Carlo (MLMC) on stochastic Burgers’ equation by using component-by-component algorithm (CBC). CBC algorithm is developed by the concept of circulant matrix that reduces the cost as a Quasi Monte Carlo technique from O(s n) to O(s n log n) where s is the dimension of integral with equi-distributed points. In this paper, Burgers’ equation is discretized using the finitevolume technique, the MLMC with different random samples is applied and the stability is tested. The results show that MLMC is suitable only for some cases of stochastic differential equations (SDEs) when using pseudo random generator, which is Monte Carlo with high cost than using CBC.