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

Abstract

SummaryHighly 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.