Lattice Boltzmann Methods for Real Time Simulations of Complex Physics, blood flow

在许多工业、生物、环境和地球物理过程中，都会遇到有或没有传热传质的复杂物理和多相流；例如，血液在可变形的通道中流动。血液由红细胞、白细胞和血小板组成。这些不相容的粒子是可变形的，漂浮在等离子体中，等离子体在弹性通道中流动，这进一步增加了问题的复杂性。近年来，人们对应用晶格玻尔兹曼方法（LBM）求解流动问题越来越感兴趣，它已成为解决物理问题的一种强有力的技术。LBM易于编码，并且具有允许包含多物理场来解决手头问题的灵活性。然而，这种方法相对较新；它还有很大的扩展空间，特别是在多物理场领域。本文的主要目的是：了解复杂血流在可变形和非光滑血管中的物理特性，以模拟真实的血流。同时，研究与血液流动有关的热量和质量传递。一般来说，需要开发和解决更现实的特定和多相流动的血流模型，从而增强我们对血流阻塞、药物输送过程和与之相关的健康问题的物理理解。它的目的是利用基于离散方法的统一方法，即LBM，为这些系统开发数学模型。开发的模型将应用于具体问题（血液流动、生物细胞流动、油和水滴等）。此外，该模型将利用LBM的局部特性，利用带有图形卡的多处理器计算机来加速实时仿真。长期目标是开发一个统一的平台来模拟流体流动和固体相互作用，具有可视化界面，实时仿真。此外，将进行实验室规模的实验来验证所开发的模型。实验数据和流动可视化将有助于加强我们对所考虑的复杂现象的物理理解。该项目将培养几名研究生，并为他们解决多学科、具有挑战性的工业/生物问题做好准备。

Complex physics and multi-phase flows with and without heat and mass transfer can be encountered in many industrial, biological, environmental, and geophysical processes; for instance, blood flow in deformable channels. The blood consists of red and white blood cells and platelets. These immiscible particles are deformable and float in a plasma which flows in elastic channels, adding further complexity to the problem. Recently, there has been a growing interest in applying the Lattice Boltzmann method (LBM) to solve flow problems, which has emerged as a powerful technique to tackle physical problems. The LBM is easy to code, and enjoys the flexibility of allowing the inclusion of multi-physics to solve the problems at hand. However, the method is relatively new; much room remains for expanding it, especially in the realm of multi-physics. The main objectives of this proposal are: to understand the physics of complex blood flows in deformable and non-smooth vessel to mimic a real blood flow. Also, to study heat and mass transfer associated with blood flow. More realistic models for blood flow in specific and multiphase flows in general need to develop and solve, which enhance our understanding the physics of blood flow blockage, drug delivery processes and health problems associated with it. It is intended to develop mathematical models for such systems using a unified approach based on discrete method, the LBM. The developed models will be applied to specific problems (blood flow, flows in biological cells, oil and water droplets, etc.). Also, the model will take advantage of the local nature of LBM to utilize multi-processor computers with graphic card to speed real time simulations. The long-term objective is to develop a unified platform to model fluid flow and solid interaction with visual interface, real time simulation. Moreover, lab scale experiments will be performed to validate the developed models. The experimental data and flow visualizations will add to reinforce our understanding of the physics of the complex phenomena under consideration. The project will train several graduate students and prepare them for solving multi-disciplinary, challenging industrial/biological problems.