2009-08-012024-05-17https://scholars.lib.ntu.edu.tw/handle/123456789/681125Abstract: I. Scientific exploration of nonlinear physical details and stability in three-dimensional fluid/heat transfer transports (Leader: Wen-Hann Sheu) 1. Construct a mathematical model to explore bifurcation scenario in a thermally driven cavity. 2. Perform an intensive computation to reveal flow/thermal bifurcations, which include Hopf, pitchfork and pseudo-periodic bifurcations. II. Scientific computing for assisting the planning of liver tumor therapies (Leader: Wen-Hann Sheu) 1. Develop a three-field (or acoustics-thermal-flow fields) coupling model for predicting temperature distribution due to can externally applied ultrasound incident wave. 2. Develop a three-point sixth-order accurate compact scheme to predict nonlinear Westervelt equation in conditions of high-frequency.