Developing a unified FVE‐ALE approach to solve unsteady fluid flow with moving boundaries

Abstract

SUMMARYIn this study, an arbitrary Lagrangian-Eulerian (ALE) approach is incorporated with a mixed finitevolume-element (FVE) method to establish a novel moving boundary method for simulating unsteady incompressible flow on non-stationary meshes. The method collects the advantages of both finite-volume and finite-element (FE) methods as well as the ALE approach in a unified algorithm. In this regard, the convection terms are treated at the cell faces using a physical-influence upwinding scheme, while the diffusion terms are treated using bilinear FE shape functions. On the other hand, the performance of ALE approach is improved by using the Laplace method to improve the hybrid grids, involving triangular and quadrilateral elements, either partially or entirely. The use of hybrid FE grids facilitates this achievement. To show the robustness of the unified algorithm, we examine both the first-and the second-order temporal stencils. The accuracy and performance of the extended method are evaluated via simulating the unsteady flow fields around a fixed cylinder, a transversely oscillating cylinder, and in a channel with an indented wall. The numerical results presented demonstrate significant accuracy benefits for the new hybrid method on coarse meshes and where large time steps are taken. Of importance, the current method yields the second-order temporal accuracy when the second-order stencil is used to discretize the unsteady terms.

A reduced domain strategy for local mesh movement application in unstructured grids

“…In reality, the users need to repeat the grid movement computations and procedures many times during their simulation steps, which may take a long time to be fulfilled [1,5,12,13,15,19,24,28,29,31,33,39,43,44,51]. Therefore, the current achieved performances are much higher in real practical problems, where grid computations are very heavy and may need several hours of computations.…”

“…There are many fluid flow simulations, such as the aerodynamics shape optimization [1,13], fluid-structure interaction [24,43], store separation [15,19], moving objects [31,44], and free surface flows [12,28], in which the grid movement is mandatory. In such fluid flow simulations, the computational domain should be suitably moved to account for the deformation occurred at its boundaries.…”

Extending a Hybrid Finite-Volume-Element Method to Solve Laminar Diffusive Flame

“…They derived two mass flux per volume expressions at the cell interfaces and treated the steady and unsteady flows on a collocated grid arrangement. Naderi et al [25] implemented an arbitrary Lagrangian-Eulerian (ALE) approach and solved the unsteady incompressible flow on nonstationary meshes using the PIS scheme. Darbandi and Fouladi [69,70] proposed a new mesh movement strategy, which could be later used to implement the PIS scheme in solving the fluid-solid interaction (FSI) problems.…”

“…They used a fully implicit hybrid FVE method and employed the modified bilinear FE interpolators to provide data during the refining and coarsening stages. Naderi et al [25] used an arbitrary Lagrangian-Eulerian (ALE) approach in the context of the FVE method and simulated unsteady incompressible flow on nonstationary meshes. Tan and Pillai [26] simulated the reactive flow in liquid composite molding using a flux-corrected transport-based FVE method.…”

Parallelization of an Unsteady ALE Solver with Deforming Mesh Using OpenACC

“…This kind of problems is termed as dynamic mesh problems in unsteady calculations. So far various kinds of dynamic mesh approaches [3,[5][6][7][8] have been proposed and validated.…”