Meshless simulation of stochastic advectiondiffusion equations based on radial basis functions
In this paper, a numerical technique is proposed for solving the stochastic advectiondiffusion equations. Firstly, using the finite difference scheme, we transform the stochastic advectiondiffusion equations into elliptic stochastic partial differential equations (SPDEs). Then the method of radial basis functions (RBFs) based on pseudospectral (PS) approach has been used to approximate the resulting elliptic SPDEs. In this study, we have used generalized inverse multiquadrics (GIMQ) RBFs, to approximate functions in the presented method. The main advantage of the proposed method over traditional numerical approaches is directly simulating the noise terms at the collocation points in each time step. To confirm the accuracy of the new approach and to show the performance of the selected RBFs, four examples are presented in one, two and three dimensions in regular and irregular domains. For test problems the statistical moments such as mean, variance and standard deviation are computed.
stochastic advectiondiffusion equations radial basis functions stochastic partial differential equations meshless method pseudospectral method