A Characteristic Galerkin Method for Discrete Boltzmann Equation

The characteristic Galerkin finite element method for the discrete Boltzmann equation is presented to simulate fluid flows in complex geometries. The inherent geometric flexibility of the finite element method permits the easy use of simple Cartesian variables on unstructured meshes and the mesh clustering near large gradients. The characteristic Galerkin procedure with appropriate boundary condition results in accurate solutions with little numerical diffusion. Several test cases are conducted, including unsteady Couette flows, lid-driven cavity flows, and steady flow past a circular cylinder on unstructured meshes. The numerical results are in good agreement with previous analytical (if applicable), numerical, and experimental results.