Lead Investigators : Drs. Chandra, Gelb, Tam, van Dommelen, and Wang
Research efforts are to be concentrated, initially, on the formulation and numerical solution of (i) multi-scale problems and (ii) moving boundary problems.
Research in material properties, in flow noise generation and in biofluid dynamics all face the problem of having to deal with large disparities in length scales. A solid may be viewed as a collection of molecules (molecular description,) as a collection of grains separated by grain boundaries (micro-scale description), or as a continuum (macroscopic description). The appropriate length scales vary from the molecular spacing, over the grain size, to the full size of the object. Related problems exist in acoustics. Most flow noise is generated by turbulence, and the spectrum of scales of turbulence is extremely wide. From fine-scale eddies to large turbulent structures, the relevant scale can differ by many orders of magnitude. In biofluid dynamics, the scale of fluid transport in and around a cell and that for blood flow in an organ differs enormously. Although the origin of the above mentioned problems are different, mathematically and computationally they are all multi-scale problems. They share many common characteristics and can greatly benefit, therefore, from interdisciplinary interactions and collaboration.
Blood cells undergo an incredible amount of deformation when squeezed through a capillary artery. This is just one of the many moving boundary problems in biofluid dynamics. Crack propagation and failure is an outstanding problem in material research. Computationally, it too is a moving boundary problem. In hydro-acoustics and in the aircraft interior noise problem, sound is generated by the motion of the wall panels caused by boundary layer turbulence. To calculate the intensity of the radiated sound, one has to find the motion of the panel surface, i.e. solve a moving boundary problem. From a methodological point of view, all these problems are similar. Effective methods for solving one of these problems can be very useful for solving other problems.