中文摘要：

将流体力学中的有限体积法（FVM）基本理论与刚黏塑性流动理论相结合，建立了基于非正交结构网格的铝型材挤压过程有限体积法数值模拟模型。模型采用非正交结构网格拟合复杂几何形状边界，可实现局部细化；在非正交网格上直接离散直角坐标系下的控制方程，避免了采用适体坐标系带来的复杂坐标转换问题。采用SIMPLE算法耦合求解压力场和速度场，推导了非正交网格上的压力修正方程。开发了铝型材非稳态挤压有限体积法数值模拟程序AE-FVM，并对典型薄壁铝型材挤压过程进行了模拟和模具优化，通过将模拟结果与基于有限体积法的模拟软件MSC／SuperForge的结果进行比较，验证了所建立的数学模型的正确性。

英文摘要：

The mathematic model of aluminum extrusion processes using FVM was established by FVM basic theories and rigid--plastic flow theories. Non--orthogonal structural grids were used to match complex geometric boundaries and local refinement of grids was also realized. The complicated coordinate transformation was avoided by diseretizing the governing equations on non--orthogonal grids directly. Pressures and velocities were calculated by using SIMPLE（semi--implicit method for pressure--linked equations）method, and pressure--corrected equations were deduced. A simulation program AE--FVM was developed based on the above fundamentals. A typical thin--walled aluminum profile extrusion process was simulated and the extrusion die was optimized by using AE--FVM and FVM software MSC/SuperForge respectively, and the comparisons of the results show that the mathematic model established herein is of feasibility and exactness.