Author(s): J. Q. Deng; M. S. Ghidaoui; K. Xu
Linked Author(s): Mohamed S. Ghidaoui
Keywords: Scalar transport; Advection; Contaminant transport; Boltzmann equation; Entropy production; Numerical oscillations; High order schemes; Finite volume
Abstract: A one and two dimensional Boltzmann-theory based model for advection-dominated mass transport problems is developed in this paper. This microscopic Boltzmannbased model offers a number of computational advantages over the classical macroscopic advection model. A second order centered finite volume technique is used to solve the proposed collisional Boltzmann based equation. In this model, the transported scalar is updated through solving the collisional Boltzmann equation for the nonequilibrium particle distribution function from which the macroscopic flux is obtained. Because of the intrinsic multidimensional and upwinding characteristics of the Boltzmann equation, no splitting or upwinding technique is required in the numerical formulation. In addition, no monotonicity constraint is used in the proposed model. Numerical experiments show that the proposed second-order Boltzmann-theory based model produces results that are as accurate as or better than the third-order ULTIMATE schemes. Furthermore, the waviness error is in most cases much smaller than that of high order ULTIMATE schemes.