Essentially Non-Oscillatory Numberical Methods For Devices Simulations

Shu 9214488这项研究的目的是开发准确和稳定的算法，基本上无振荡（ENO）的方法的基础上，这是最初设计的一般双曲守恒定律，特别是可压缩的欧拉方程在气体动力学，设备模拟在两个，并最终在三维空间。 重点将 对流体动力学（HD）模型和最近发展的能量输运（ET）模型进行了模拟，并探讨了它们的物理应用。 与器件模拟相关的问题，例如基于物理和数值考虑的边界条件的选择，边界层和内层的适当处理（高梯度区域），适当处理由于边界条件引起的势中的轻度奇异性，适当处理可能的刚性源项，并研究了该算法的并行实现。 努力的最终目标是开发一种数值算法，这是准确和强大的，不仅适用于设备模拟使用的HD和ET模型，但也其他模型。 相关模型的物理应用也将与其他应用数学家，设备物理学家和工程师合作进行研究。 ***

Shu 9214488 The objective of this proposed research is to develop accurate and stable algorithms, based on the essentially non-oscillatory (ENO) methodology, which were originally designed for general hyperbolic conservation laws and in particular for the compressible Euler equations in gas dynamics, to device simulations in two and eventually in three space dimensions. The emphasis will be on simulating the hydrodynamioc (HD) model and the recently developed Energy-Transport (ET) model and investigating their physical applications. Issues related to device simulations, such as the choice of boundary conditions based upon physical as well as numerical considerations, the adequate handling of boundary and inner layers (high gradient regions), the adequate handling of mild singularities in the potential due to the boundary conditions, the adequate handling of possibly stiff source terms, and parallel implementation of the algorithm will be investigated. The eventual goal of the effort is to develop a numerical algorithm which is accurate and robust, suitable for device simulations using not only the HD and ET models but also other models as well. Physical applications of related models will also be investigated in collaboration with other applied mathematicians, device physicists and engineers. ***