Phase transitions in thermoelasticity and compressible fluids

本计画主要探讨在形状记忆合金微结构发展、可压缩流体气液转换、天体物理中子星形成过程中所产生的动态相变问题。所有这些现象的数学锐界面模型是双曲椭圆守恒律系统。发展了求解二维/三维守恒律方程的局部自适应有限体积法。新的方法是通过水平集（LS）技术来演化相边界。代码将在测试问题上进行验证，嵌入到并行环境中，并应用于特定问题。将分析该方法的稳定性和收敛性。

This project deals with dynamic phase transition problems arising in shape memory alloys developing microstructure, in compressible fluids undergoing gas-liquid-transitions, or during the formation of neutron stars in astrophysics. The mathematical sharp-interface model for all these phenomena are systems of hyperbolic-elliptic conservation laws. A locally adaptive finite volume method (FVM) to solve the conservation laws in 2D/3D will be developed. The novel approach is to evolve the phase boundary by a level set (LS) technique. The code will be validated on test problems, embedded into a parallel environment, and applied to specific problems. The method will be analyzed with respect to stability and convergence.