The objective of this paper is to investigate the condition number of various formulations of LSFEM （least-squares finite element method） for SWE （shallow-water equations）, and develop a better conditioned shallow...The objective of this paper is to investigate the condition number of various formulations of LSFEM （least-squares finite element method） for SWE （shallow-water equations）, and develop a better conditioned shallow-water model to simulate current structure interactions. Various formulations of LSFEM for a two-dimensional vertically-averaged non-viscous shallow-water equations can be constructed, depending on the choice of norm, variables, interpolations, and possible treatment of boundary conditions. The condition number of the resulting system of equations is systematically examined and compared. It is found that condition number of the resulting system of equations depends on the choice of variables, interpolations, and size of element （h）. Order reduction （UW） formulations, with introducing auxiliary variables, with low-order interpolation is better conditioned and more efficient than direct （U） formulation with high-order interpolation. However, to resolve large gradients and fine structures of flow filed, high-order methods are generally preferred. The developed shallow-water model is used to simulate flow past an elliptic hump and flow past a cylinder. Computed results are compared with other numerical solutions.展开更多
文摘The objective of this paper is to investigate the condition number of various formulations of LSFEM （least-squares finite element method） for SWE （shallow-water equations）, and develop a better conditioned shallow-water model to simulate current structure interactions. Various formulations of LSFEM for a two-dimensional vertically-averaged non-viscous shallow-water equations can be constructed, depending on the choice of norm, variables, interpolations, and possible treatment of boundary conditions. The condition number of the resulting system of equations is systematically examined and compared. It is found that condition number of the resulting system of equations depends on the choice of variables, interpolations, and size of element （h）. Order reduction （UW） formulations, with introducing auxiliary variables, with low-order interpolation is better conditioned and more efficient than direct （U） formulation with high-order interpolation. However, to resolve large gradients and fine structures of flow filed, high-order methods are generally preferred. The developed shallow-water model is used to simulate flow past an elliptic hump and flow past a cylinder. Computed results are compared with other numerical solutions.
