Phase transitions in thermoelasticity and compressible fluids

热弹性和可压缩流体中的相变

• 批准号: 5363366
• 负责人: Professor Dr. Dietmar Kröner
• 金额: --
• 依托单位: Mathematisches Institut
• 依托单位国家: 德国
• 项目类别: Research Units
• 财政年份: 2002
• 资助国家: 德国
• 起止时间: 2001-12-31 至 2009-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5363366?language=en
• 关键词: Phase; transitions; thermoelasticity; compressible; fluids

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.

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。