A 3D implicit immersed boundary method with application

研究了一种三维隐式浸入边界（IB）方法及其并行实现。IB方法已被广泛用于模拟涉及弹性结构和不可压缩粘性流体相互作用的问题。由于显式IB方法有吸引力的相对简单性，该方法的许多显式版本已在实践中使用。然而，显式IB方法有一个缺点：时间步长必须很小，以保持浸入固体边界的数值稳定性，这在计算成本上并不经济，特别是对于三维问题。研究者开发了一种三维隐式IB方法，通过实现隐式方案来计算浸入边界传递给流体的力，并更新实体边界配置。由于基本变量的拉格朗日和欧拉混合描述及其复杂的相互关系，每个时间步必须求解一个高度非线性的代数方程组以推进解。为了降低三维隐式IB方法的复杂性并便于并行实现，采用晶格玻尔兹曼方法（D3Q19模型）求解不可压缩粘性Navier-Stokes方程。此外，研究者还研究了一种基于问题固有性质的加速非线性代数方程组解的有效预条件。研究者应用新的隐式IB方法来研究与有限厚度的柔性片浸入流动的粘性流体相关的减阻过程。目标是建立阻力与迎面而来的流速、雷诺数、无因次弯曲模量和无因次质量密度有关的标度定律。更高级的应用包括初级纤毛和内皮表面层与粘性移动流体相互作用的建模和模拟。自然界有很多涉及柔体和流体相互作用的问题（例如，空中飘扬的旗帜）。这种相互作用是科学和工程中非常复杂且尚未被很好理解的广泛现象的基础。利用现代超级计算机进行大规模科学计算，研究了一种研究流-柔-体相互作用的数值方法。该方法适用于科学和生物医学工程中的许多重要问题。一个直接的应用是研究由身体柔韧性引起的阻力减少。水下推进的主要能量消耗用于克服周围流体的阻力（阻力）。水动力设计的一个目的是减少浸没体（如车辆）所经历的阻力。减少阻力意味着提高推进效率和降低能源成本。研究者的研究可能会启发新的水下推进技术设计的产生和发展，提高效率和速度。更复杂的应用包括建模和模拟上皮细胞的初级纤毛与肾小管中移动的粘性液体的相互作用，这与多囊肾病有关，以及研究动脉粥样硬化（心脏病发作和中风的主要原因）的起源，在动脉粥样硬化中，血液流动与运输和反应成分与由内皮表面层覆盖的柔顺血管壁相互作用。这些应用可能导致对多囊肾病和动脉粥样硬化的更深入的了解。

The investigator studies a 3D implicit immersed boundary (IB) method and its parallel implementation with applications. The IB method has been widely used to simulate problems involving interactions of an elastic structure and an incompressible viscous fluid. Because of the attractive relative simplicity of an explicit IB method numerous explicit versions of the method have been used in practice. However, an explicit IB method has a drawback: the time-step size must be small to maintain numerical stability of the immersed solid boundary which is not economical in computational cost, especially for three dimensional problems. The investigator develops a 3D implicit IB method by implementing an implicit scheme for computing forces imparted by the immersed boundary to the fluid and for updating the solid boundary configuration. Because the mixed Lagrangian and Eulerian descriptions of the fundamental variables and their complicated interconnections, a highly nonlinear algebraic system of equations has to be solved for each time step to advance the solution. In order to reduce the complexity of the 3D implicit IB method and to facilitate its parallel implementation, the lattice Boltzmann method (the D3Q19 model) is used to solve the incompressible viscous Navier-Stokes equations. In addition, The investigator studies an efficient preconditioner based on inherent properties of the problem for expediting the solution of the nonlinear algebraic system of equations. The investigator applies the new implicit IB method to investigate the drag reduction process associated with a flexible sheet of finite thickness immersed in a flowing viscous fluid. The objective is to develop scaling laws for drag with respect to oncoming flow speed, Reynolds number, dimensionless bending modulus and dimensionless mass density. More advanced applications include modeling and simulation of the primary cilia and the endothelial surface layer interacting with viscous moving fluids.Nature is very rich in problems involving interactions of a flexible body and a fluid (e.g., a flapping flag in the air). Such interactions underlie a wide range of phenomena in science and engineering which are very complicated and not yet well understood. The investigator studies a numerical method for investigating the fluid-flexible-body-interaction through large-scale scientific computing using modern supercomputers. The method is applicable to many important problems in science and biomedical engineering. One immediate application is study of drag reduction induced by body flexibility. The major energy expense for underwater propulsion is used for overcoming the resistance (drag) of ambient fluid. One aim of a hydrodynamic design is to reduce the drag experienced by an immersed body (e.g. a vehicle). Reduced drag means improved propulsion efficiency and lowered energy cost. The investigator's study may inspire genesis and development of novel designs of underwater propelling technologies with improved efficiency and increased speed. More sophisticated applications include modeling and simulations of the primary cilia of the epithelial cells interacting with the moving viscous fluid in the kidney tubules, which is related to the polycystic kidney disease, and studying the genesis of atherosclerosis (leading cause of heart attacks and stokes) in which blood flow with transport and reacting constituents interacting with a compliant vessel wall covered by an endothelial surface layer.Such applications may lead to greater understandings of the polycystic kidney disease and the atherosclerosis.