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

Abstract

Summary Highly nonlinear, turbulent, dynamic, fluid‐structure interaction problems characterized by large structural displacements and deformations, as well as self‐contact and topological changes, are encountered in many applications. For such problems, the Eulerian computational framework, which is often equipped with an embedded (or immersed) boundary method for computational fluid dynamics, is often the most appropriate framework. In many circumstances, it requires the computation of the time‐dependent distance from each active mesh vertex of the embedding mesh to the nearest embedded discrete surface. Such circumstances include, for example, modeling turbulence using the Spalart‐Allmaras or detached eddy simulation turbulence models and performing adaptive mesh refinement in order to track the boundary layer. Evaluating at each time step the distance to the wall is computationally prohibitive, particularly in the context of explicit‐explicit fluid‐structure time‐integration schemes. Hence, this paper presents two complementary approaches for reducing this computational cost. The first one recognizes that many quantities depending on the wall distance are relatively insensitive to its inaccurate evaluation in the far field. Therefore, it simplifies a state‐of‐the‐art algorithm for computing the wall distance accordingly. The second approach relies on an effective wall distance error estimator to update the evaluation of the wall distance function only when otherwise, a quantity of interest that depends on it would become tainted by an unacceptable level of error. The potential of combining both approaches for dramatically accelerating the computation of the wall distance is demonstrated with the Eulerian simulation of the inflation of a disk‐gap‐band parachute system in a supersonic airstream.

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

“…The asymptotic complexity of the FMM and other marching type methods is , which is a substantial improvement over that of the naive approach. However, it was shown in the work of Grimberg and Farhat that for unsteady, viscous, FSI computations based on the SA turbulence model, which requires the computation of the distance to the wall, performed using explicit‐explicit time stepping, which is typically the most robust and efficient approach for simulating highly nonlinear unsteady FSI problems with potentially material failure (for example, see the works of Wang et al and Farhat et al), the cost of the computation of the distance to the wall using a fast marching type method can dominate the total computational cost of an Eulerian FSI simulation performed using an EBM, even in the absence of AMR.…”

“…Here, it is noted that as far as the proposed AMR framework is concerned, the accuracy of the computation of the distance to the wall matters primarily for the mesh adaptation criterion based on this distance (see Algorithm 1), which is in the boundary layer and its vicinity. In this case, an economical estimation of the distance function f ( X ), where , rather than the function itself can be computed, for example, using the fast approximate distance algorithm presented in the work of Grimberg and Farhat . This algorithm offers an even lower computational complexity than all aforementioned methods, but at the expense, in the worst case scenario, of a small degradation of the accuracy of the computed distance to the wall in the far field.…”

“…It performs a single pass over the fluid mesh vertices ordered by mesh layer starting from the embedded surface, requires only the existing mesh connectivity data structure, does not perform any sorting of any data structure, and thus has a reduced computational complexity of . When the mesh element size varies only as a function of its distance from the embedded surface, the mesh‐layer‐based vertex sorting reduces to sorting by the vertex distance value: In this case, the estimation algorithm presented in the work of Grimberg and Farhat becomes essentially a faster variant of the FMM. This type of mesh element size variation is typical of most CFD meshes, including those resulting from the AMR framework described above.…”

“…This type of mesh element size variation is typical of most CFD meshes, including those resulting from the AMR framework described above. Thus, the fast distance estimation algorithm described in the work of Grimberg and Farhat provides a useful means for computing more efficiently the distance to the wall in general, and accelerating Algorithm 1 in particular.…”

“…Still, for unsteady simulations where the position of the embedded surface is time dependent and thus the distance to the wall must be recomputed at each time step, it was also shown in the work of Grimberg and Farhat that the computational cost of even the fast aforementioned distance estimation algorithm can represent an unacceptable fraction of the total cost of an explicit‐explicit viscous FSI simulation based on the SA turbulence model, and performed using an Eulerian EBM without AMR. For this reason, a predictor‐corrector scheme for estimating the value of the distance to the wall based on updating this estimation only when otherwise a QoI that depends on it would become tainted by an unacceptable level of error, was also proposed in the work of Grimberg and Farhat . This scheme reduces significantly the overhead associated with computing the distance to the wall by adapting the frequency of reevaluating the distance function.…”