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A numerical model of the lattice Boltzmann method ͑LBM͒ utilizing least-squares finite-element method in space and the Crank-Nicolson method in time is developed. This method is able to solve fluid flow in domains that contain complex or irregular geometric boundaries by using the flexibility and numerical stability of a finite-element method, while employing accurate least-squares optimization. Fourth-order accuracy in space and second-order accuracy in time are derived for a pure advection equation on a uniform mesh; while high stability is implied from a von Neumann linearized stability analysis. Implemented on unstructured mesh through an innovative element-by-element approach, the proposed method requires fewer grid points and less memory compared to traditional LBM. Accurate numerical results are presented through two-dimensional incompressible Poiseuille flow, Couette flow, and flow past a circular cylinder. Finally, the proposed method is applied to estimate the permeability of a randomly generated porous media, which further demonstrates its inherent geometric flexibility.

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A web‐based environment is utilized as a means to introduce advanced mass transfer processes concepts in environmental engineering and science courses. System development and implementation is presented, including detailed descriptions of the techniques employed to link software written in high‐level computer languages such as C++ and FORTRAN to an internet‐based, user‐friendly graphical user interface for both program input and output. © 2003 Wiley Periodicals, Inc. Comput Appl Eng Educ 11: 25–39, 2003; Published online in Wiley InterScience (www.interscience.wiley.com); DOI 10.1002/cae.10036

In our previous efforts, a least squares finite element lattice Boltzmann method (LSFE-LBM) was developed and successfully applied to simulate fluid flow in porous media. In this paper, we extend LSFE-LBM to simulate solute transport in bulk fluid and couple it with non-linear sorption/desorption processes at solid particle surfaces. The influences of the Peclet number and sorption non-linearity on solute transport is evaluated. Results of this work demonstrate the capability of using LSFE-LBM to study fluid flow and non-linear mass transfer processes at the pore scale.