Discretizing a solution in the Fourier domain rather than the time domain presents a significant advantage in solving transport problems that vary smoothly and periodically in time, such as cardiorespiratory flows. The finite element solution of the resulting time-spectral formulation is investigated here for the convection-diffusion equations. In addition to the baseline Galerkin's method, we consider stabilized approaches inspired by the streamline upwind Petrov/Galerkin (SUPG), Galerkin/least square (GLS), and variational multiscale (VMS) methods. We also introduce a new augmented SUPG (ASU) method that, by design, produces a nodally exact solution in one dimension for piecewise linear interpolation functions. Comparing these five methods using 1D, 2D, and 3D canonical test cases shows while the ASU is most accurate overall, it exhibits stability issues in extremely oscillatory flows with a high Womersley number in 3D. The GLS method, which is identical to the VMS for this problem, presents an attractive alternative due to its excellent stability and reasonable accuracy.
翻译:暂无翻译
亚利桑那州立大学(Arizona State University)是全美最大最佳的五所“大学城”之一,创立于1885年,坐落于距州府凤凰城11英里的大学城坦佩。
亚利桑那州立大学学术力量雄厚,教学一流,被誉为全美州立大学中研究密度最高的大学之一,是全球性跨学科教学和研究的重要中心。其商学院和教育学院排名全美前列。此外,天文学也是亚利桑那州立大学名牌系科。