An Adaptive Mesh Refinement Concept for Viscous Fluid-Structure Computations Using Eulerian Vertex-Based Finite Volume Methods

Abstract

Embedded Boundary Methods (EBMs) [1] for the solution of Computational Fluid Dynamics (CFD) and Fluid-Structure Interaction (FSI) problems are typically formulated in the Eulerian setting, which makes them more attractive than Chimera and Arbitrary Lagrangian-Eulerian methods when the structure undergoes large structural motions and/or deformations. In the presence of viscous flows however, they necessitate Adaptive Mesh Refinement (AMR) because unlike Chimera and ALE methods, they do not track boundary layers [2]. In general, AMR gives rise to non-conforming mesh configurations that can complicate the semi-discretization process. This is the case when this process is carried out using the popular vertex-based finite volume method and dual cells. Perhaps for this reason, most of the literature on AMR in the context of EBMs and the FV method has focused so far on cell-centered schemes, where the treatment of non-conforming mesh configurations is straightforward [1]. Specifically, most if not all local refinement strategies developed in this context generate "hanging" nodes in the refined mesh that can be easily dealt with using cell-centered but not vertex-based methods. In the latter case, flux assembly after a mesh refinement step becomes a problematic issue, due to presence of dual cells. This talk proposes a simple approach for resolving this issue by appropriately managing the construction of dual cells past each refinement step. The talk will recall the motivations for EBMs and vertex-based FV methods, explain the aforementioned AMR issue that arises in their context, present a method for resolving it, and illustrate this method with the application of the EBM known as FIVER (Finite Volume method with Exact two-phase Riemann solvers) [3, 4] to various examples including the prediction of the aerodynamic performance of a Formula 1 car.

Fast computation of the wall distance in unsteady Eulerian fluid‐structure computations

“…One example is the use of the wall distance function to represent in a turbulence model the wall's effect on the eddy viscosity destruction that occurs inside the boundary layer. Another example is the computation of the wall distance to enable AMR within the boundary layer regions in FSI computations on non body‐fitted meshes . In such applications, it is deemed acceptable to introduce approximations into the numerical method chosen for solving the BVP that enable a faster evaluation of the wall distance function, at the expense of potentially sacrificing some of the accuracy of the wall distance solution in the far field.…”

“…Another example is the computation of the wall distance to enable AMR within the boundary layer regions in FSI computations on non body-fitted meshes. 15 In such applications, it is deemed acceptable to introduce approximations into the numerical method chosen for solving the BVP (1) that enable a faster evaluation of the wall distance function, at the expense of potentially sacrificing some of the accuracy of the wall distance solution in the far field. Such approximations are particularly welcome if, in addition, they improve the parallel efficiency and scalability of the numerical method.…”

“…Many applications of computational fluid dynamics (CFD) require the evaluation, for all vertices in the discretized computational fluid domain, of the distance function to the nearest wall boundary (or simply, the wall distance). These include, among others, turbulence modeling for Reynolds‐averaged Navier‐Stokes (RANS) simulations, zonal RANS and detached eddy simulation methods, interface tracking and level set methods for Eulerian fluid‐structure interaction (FSI) and multimaterial computations, boundary layer and overset mesh generation, and adaptive mesh refinement (AMR) . A brute force approach for evaluating the wall distance that repeats a search over all vertices discretizing the wall boundary for every vertex of the fluid mesh is typically inadequate, due to its large asymptotic computational complexity, which is O ( N w N i ), where N w is the number of vertices of the discrete representation of the wall and N i is the number of vertices in the interior of the computational fluid domain.…”

“…These include, among others, turbulence modeling for Reynolds-averaged Navier-Stokes (RANS) simulations, 1-3 zonal RANS and detached eddy simulation methods, 4,5 interface tracking and level set methods for Eulerian fluid-structure interaction (FSI) and multimaterial computations, [6][7][8][9][10] boundary layer and overset mesh generation, 11,12 and adaptive mesh refinement (AMR). [13][14][15] A brute force approach for evaluating the wall distance that repeats a search over all vertices discretizing the wall boundary for every vertex of the fluid mesh is typically inadequate, due to its large asymptotic computational complexity, which is O(N w N i ), where N w is the number of vertices of the discrete representation of the wall and N i is the number of vertices in the interior of the computational fluid domain. Moreover, such an approach may be inaccurate if the nearest point on the wall to a vertex of the interior fluid mesh is not a vertex of the wall surfacic mesh.…”

Mesh adaptation framework for embedded boundary methods for computational fluid dynamics and fluid‐structure interaction

“…Hence, the main objective of this paper is to present an AMR framework for EBMs that is applicable to highly nonlinear FSI applications, can operate on unstructured as well as structured meshes, and maintains in all cases mesh conformity. This framework, a preliminary version of which was recently overviewed in the conference paper, allows EBMs to track the boundary layer, locate flow features such as shocks, vortices, and wakes and keep them at all time instances resolved. It is based on local coarsening and refinement techniques and therefore is amenable to parallel implementation.…”