Mathematical Sciences: Systems of Nonlinear Conservation Laws

该研究计划涉及理论 非线性偏微分方程组的数值研究 通过失去严格双曲性而改变类型的方程。 具体的努力包括调整和执行 新出现的激波捕捉高精度的数值方法。 这就涉及到广义黎曼的近似解 最近的理论见解获得的问题， 将使用PI。 导致混合方程的本构定律 类型也将被调查。 这项研究计划的结果将有应用 在多相流、弹性固体和磁电机领域， 流体力学

This research program is concerned with the theoretical and numerical study of systems of nonlinear partial differntial equations which change type by losing strict hyperbolicity. Specific efforts include the adaptation and implementation of the emerging shock capturing numerical methods of high accuracy. This involves the approximate solution of generalized Riemann problems for which recent theoretical insights obtained by the PI will be used. Constitutive laws leading to equations of mixed type will also be investigated. Results from this research program will have applications in the areas of multiphase flows, elastic solids and magneto- hydrodynamics.