Performance of fluid-structure interaction based on analytical and computational techniques

Solving coupling of fluid and solid governing equations in fluid-structure interaction (FSI) is a common computational problem well known to mathematicians, scientists and engineers. Several algorithms exist for solving this problem. However, when the approach for the FSI solution is Partitioned approach (i.e., separated solvers for fluid and solid domains), the problem may not be solvable and obtain meaningful results. In fact, it has been shown that the general problem of solving the FSI system with partitioned approach is ``Added mass instability'', i.e., extremely difficult and (it is believed) inefficient; thus, it is not suitable to be adopted for solving wide range of applications. It turns out, though, that the time integration schemes used for structural acceleration have a strong impact on the efficiency of solving FSI system of equations. It is found that amount of numerical damping can change the performance considerably. In particular, efficiency of solutions with less numerical damping in structural integration schemes is found to be superior than those with greater numerical damping. It is found out that in some cases, the value of critical relaxation factor can be increased up to approximately 30 percent by varying value of applied numerical damping. This in turn leads to a considerable reduction in computational time. However, the improvement depends largely on the density ratio. The critical value of relaxation factor becomes almost invariant with the amount of the numerical damping when density ratio is very high. Therefore, the improved efficiency can be negligible in some cases whereby working fluid is much denser than solid. Moreover, it is also discovered that the critical value of relaxation factor can be also influenced by some other factors such as fluid time integration schemes, time step size, and geometric properties. Although the FSI performance that can be improved by varying numerical damping used in the discretization schemes for structural acceleration, the change in performance is limited, especially when density ratio is quite high. Therefore, it is concluded that only a narrow range of problems can be solved by this technique. To be of practical use, Artificial compressibility is introduced for a better efficiency for a wider range of applications. It is found that this technique can speed up the solution process significantly when compared to the application of relaxation factor, regardless of the density ratio of fluid and solid. Thus, we desire to adopt Artificial compressibility for solving a realistic engineering application. A study of artherosclerosis in carotid bifurcation is achieved with this technique. Apart from the illustration of the applicability of artificial compressibility technique, the main goal of solving this particular engineering application is to answer the following questions: - What is the influence of the degree of stenosis on mechanical stress experienced in carotid bifurcation?} - How does the pattern of blood flow change with the presence of stenosis with different sizes?} - Is there any relationship between blood pressure, structural stress and deformation of the lesion? From our results, the degree of stenotic plaque can radically change the blood flow pattern and mechanical stress on the apex of stenosis. As a result, this significantly affects wall shear stress and deformation. The relationship among blood pressure, stenotic compression and deformation shows that high level of compression occurs at the stenotic apex, and can potentially be responsible for plaque progression