Qualification of uncertainty for simulating solute transport in the heterogeneous media with sparse grid collocation method

Abstract

The sparse grid collocation method is discussed to qualify the uncertainty of solute transport. The Karhunen-Loeve (KL) expansion is employed to decompose the log transformed hydraulic conductivity. The head, velocity and concentration fields are represented by the Lagrange polynomial expansion. A sparse grid collocation method is then used to reduce the original stochastic partial differential equations to a set of deterministic equations which is collocated at selected interpolation (collocation) points. The collocation points are constructed by the Smolyak algorithm. The accuracy, efficiency and convergence property of sparse grid collocation method are investigated by numerical experiments. The analysis shows that stochastic collocation strategy helps to decouple stochastic computations, and all the numerical computation is possible to be implemented by existing deterministic finite element codes. The proposed method provides an efficient way to evaluate the uncertainty of the solute transport in the heterogeneous media.