High-order embedded boundary methods for fluid-structure interaction [electronic resource]

Embedded boundary methods are gaining popularity for solving fluid-structure interaction (FSI) problems because they simplify a number of computational issues. These range from gridding the fluid domain, to designing and implementing Eulerian-based algorithms for challenging fluid-structure applications characterized by large structural motions and deformations or topological changes. However, because they typically operate on non body-fitted grids, embedded boundary methods also complicate other issues such as the treatment of wall boundary conditions in general, and fluid-structure transmission conditions in particular. These methods also tend to be at best first-order space-accurate at the embedded boundaries. In some cases, they are also provably inconsistent at these locations. To address this issue, the present work first presents a systematic approach for constructing higher-order embedded boundary methods for fluid-structure interaction problems. This approach is developed for inviscid flows and fluid-structure interaction problems. For the sake of clarity, but without any loss of generality, the methodology is described in one and two dimensions. However, its extension to three-dimensional problems is straightforward and illustrated by numerical examples. The proposed approach leads to a departure from the current practice of populating ghost fluid values independently from the chosen spatial discretization scheme. Instead, it accounts for the pattern and properties of a preferred higher-order discretization scheme, and attributes ghost values as to preserve the order of spatial accuracy of this scheme. It is illustrated in this work by its application to various finite difference (FD) and finite volume (FV) methods. Its impact is demonstrated by numerical experiments that confirm its theoretically proven ability to preserve higher-order spatial accuracy, including in the vicinity of the immersed interfaces. Next, attention is focused on a limiter issue that is associated with second-order FV methods. In most practical higher-resolution FV methods, like for example second-order MUSCL schemes, slope limiters are employed. They are designed to suppress spurious oscillations near discontinuities as well as preserve second-order accuracy in the region where the solution is sufficiently smooth. Most slope limiter functions are developed assuming one-dimensional uniform CFD grids however, are applied as such in practice to unstructured meshes. It is observed that for a cell-centered FV scheme, these conventional limiter functions lead to loss of spatial accuracy when the fluid meshes are non-uniform. To fix this issue, the Reconstruction-Evolve-Project (REP) procedure is generalized to account for non-uniform grids. The effect of slope limiters on accuracy and total- variational-diminishing (TVD) stability is also studied. A series of mathematical conditions that the slope limiters must satisfy in order to deliver desired numerical properties are derived. Several most widely used conventional slope limiter functions are enhanced to satisfy these conditions. The impact of the enhanced slope limiter functions is demonstrated by solving benchmark problems on highly non-uniform CFD meshes that confirm: (1) the ability to maintain second-order accuracy in space and (2) the ability to suppress spurious oscillations near discontinuities.

Advisor: Farhat Charbel primary advisor. Thesis advisor
Lew Adrian advisor. Thesis advisor
Papanicolaou George advisor. Thesis advisor