Recent Enhancements to the FUN3D Flow Solver for Moving-Mesh Applications

Abstract

An unsteady Reynolds-averaged Navier-Stokes solver for unstructured grids has been extended to handle general mesh movement involving rigid, deforming, and overset meshes. Mesh deformation is achieved through analogy to elastic media by solving the linear elasticity equations. A general method for specifying the motion of moving bodies within the mesh has been implemented that allows for inherited motion through parent-child relationships, enabling simulations involving multiple moving bodies. Several example calculations are shown to illustrate the range of potential applications. For problems in which an isolated body is rotating with a fixed rate, a noninertial reference-frame formulation is available. An example calculation for a tilt-wing rotor is used to demonstrate that the time-dependent moving grid and noninertial formulations produce the same results in the limit of zero time-step size.

Assessment of the Fluid-Structure Interaction Capabilities for Aeronautical Applications of the Open-Source Solver Su2.

“…First introduced by Thomas and Lombard [19], it has been shown mathematically and through numerical experiment [20][21][22] that satisfying the GCL can improve the accuracy and stability of the chosen scheme. A straightforward technique for the numerical implementation of the GCL [23,24] has been included as part of the dual-time stepping approach.…”

A Quasi-Steady Flexible Launch Vehicle Stability Analysis Using Steady CFD with Unsteady Aerodynamic Enhancement

“…25 The mesh deformation is accomplished by treating the mesh motion as analogous to a linear elasticity problem. 26 The linear elasticity equations are written in finite-volume form and evaluated in a manner similar to the integration of the conservation form of the flow equations.…”

Integrated Design of an Active Flow Control System Using a Time-Dependent Adjoint Method

“…This value has been chosen based on numerical experience and represents a compromise between temporal accuracy and computational cost. Ideally, an error-based subiterative controller such as that described in [6] would be used; such an approach is available for the solution of (2.4), but has not been implemented for (3.4). The effect of time step size was investigated and it was found that the asymptotic mean value of the lift coefficient did not change significantly using more than 100 steps per blowing cycle.…”

“…The mesh is modeled as an elastic medium that obeys the elasticity relations of solid mechanics, where an auxiliary system of linear partial differential equations (PDEs) is solved to determine the mesh coordinates after each shape update. Discretization of these PDEs yields a linear system of equations: 6) where K represents the elasticity coefficient matrix and X is the vector of updated surface coordinates, complemented by zeros for all interior coordinates. Thus for the static grid formulation used here, the grid operator takes the specific form:…”

“…References [1,6,13,29] describe the flow solver used in the current work. The code can be used to perform aerodynamic simulations across the speed range and an extensive list of options and solution algorithms is available for spatial and temporal discretizations on general static or dynamic mixed-element unstructured meshes which may or may not contain overset grid topologies.…”