Isogeometric variational multiscale modeling of stably stratified flow over complex terrains

Abstract

Numerical modeling of stratified boundary layer over complex terrain has been an ongoing challenge in the field of environmental fluid dynamics. In this work, we present a computational framework aiming to tackle that challenge. The key components of the framework are residual-based variational multiscale method, isogeometric analysis, and weak imposition of Dirichlet boundary condition. The framework is validated against a laboratory experiment on strongly stratified flow past a three-dimensional bell-shaped hill. Good agreement is observed for qualitative flow physics, with the predicted occurrences of flow separation, recirculation, and hydraulic jump closely matching those in the experiment. In addition, the dividing-streamline height and wavelength of lee wave computed from the present framework compare well to the theoretical predictions. We show that the present framework is able to tackle various degrees of stratifications. The effect of weak imposition of Dirichlet boundary condition on the performance of the framework is also examined. This paper is concluded with an outlook toward applying the present framework to modeling microscale stratified flow past real-world terrains by simulating stratified flow past a two-dimensional environmental terrain.