Accuracy and stability of transient multiphysics simulations

This thesis is concerned with the development of numerical methods for unsteady fluid-structure interaction problems using loosely-coupled partitioned procedures. Partitioned procedures are routinely used in the simulation of fluid-structure interaction because of the flexibility and software modularity they offer in the choice of fluid and structural solvers and in the discretization used on both sides of the interface. However, such procedures are often criticized in the computational aeroelasticity community for their lack of accuracy and sufficient numerical stability as compared to monolithic and strongly-coupled methods. The motivation for this research work is to develop a robust, accurate and stable methods for the loosely-coupled framework.; In the first part of this dissertation, the accuracy of spatial coupling across non-matching meshes is investigated for flat and curved fluid-structure interfaces. This part analyzes two types of discretization schemes for the spatial coupling: (a) point-to-element projection schemes (e.g., node-projection, quadrature-projection) and (b) the common-refinement scheme. It is shown that the point-to-element projection schemes may yield inaccurate coupling of discrete interface conditions and hence lead to weak instabilities in the form of spurious oscillations in the coupled solutions. By constructing sub-elements and applying the least-squares minimization, the common-refinement scheme resolves this problem and yields an accurate spatial coupling of discrete interface conditions across non-matching meshes. Theoretically, the accurate coupling is shown to preserve the stability of the loosely-coupled system while maintaining energy conservation over a reference interface. This is demonstrated with the fluid-structure interaction problems of increasing complexity over flat and curved interfaces. Finally, simple analytical error indicators are introduced, which correlate well with the numerical errors of the coupling schemes.; In the second part of this dissertation, a new loosely-coupled time-stepping procedure for modeling coupled fluid-structure and thermal problems is presented. The procedure relies on a higher-order Combined Interface Boundary Condition (CIBC) treatment for improved accuracy and stability of temporal coupling. Traditionally, continuity of Dirichlet and Neumann conditions along interfaces are satisfied through algebraic interface conditions applied in a staggered fashion. It is argued that, in existing time-stepping procedures, the interface undermines stability and accuracy of coupled simulations. By utilizing the CIBC technique on the Dirichlet and Neumann boundary conditions, a staggered coupling procedure is constructed with the same order of accuracy and stability of standalone computations. The correction terms for the Dirichlet and Neumann conditions can be explicitly added to the standard staggered time-stepping stencils so that the discretization is well defined across the deformable interface. The new formulation involves a coupling parameter whose value is explicitly determined by the Godunov-Ryabenkii's stability theory for the coupled thermal problem and via numerical experiments for the fluid-structure coupling. Finally, we demonstrate the validity of analysis through a two-dimensional application involving subsonic flow over a thin-shell structure.; Although the applications considered in this thesis are of two-dimensional nature, generalization issues to three-dimensional are outlined for both spatial and temporal coupling algorithms. Finally, the proposed numerical techniques are of a general character and thus could be applied to other multiphysics problems.