A block LU-SGS implicit unsteady incompressible flow solver on hybrid dynamic grids for 2D external bio-fluid simulations

SUMMARYThis paper presents a local domain-free discretization (DFD) method for the simulation of unsteady flows over moving bodies governed by the incompressible Navier-Stokes equations. The discretization strategy of DFD is that the discrete form of partial differential equations at an interior point may involve some points outside the solution domain. All the mesh points are classified as interior points, exterior dependent points and exterior independent points. The functional values at the exterior dependent points are updated at each time step by the approximate form of solution near the boundary. When the body is moving, only the status of points is changed and the mesh can stay fixed. The issue of 'freshly cleared nodes/cells' encountered in usual sharp interface methods does not pose any particular difficulty in the presented method. The Galerkin finite-element approximation is used for spatial discretization, and the discrete equations are integrated in time via a dual-time-stepping scheme based on artificial compressibility. In order to validate the present method for moving-boundary flow problems, two groups of flow phenomena have been simulated: (1) flows over a fixed circular cylinder, a harmonic in-line oscillating cylinder in fluid at rest and a transversely oscillating cylinder in uniform flow; (2) flows over a pure pitching airfoil, a heaving-pitching airfoil and a deforming airfoil. The predictions show good agreement with the published numerical results or experimental data.

Section: Flow Over a Deforming Airfoilmentioning

confidence: 97%

Section: Flow Over a Deforming Airfoilmentioning

confidence: 99%

A local domain‐free discretization method for simulation of incompressible flows over moving bodies

Zhou

Chen

2011

“…Many implicit time-integration schemes [3][4][5][6][7][8][9][10][11][12] have been developed and successfully implemented to accelerate the convergence rate. The most commonly used implicit technique in steady flow simulation is the first-order backward Euler scheme.…”

Section: Introductionmentioning

confidence: 99%

A hybrid implicit scheme for solving Navier–Stokes equations

Wang

Mian

Liu

et al. 2015

SUMMARYA hybrid implicit scheme is developed in this study to solve 3D compressible Navier-Stokes equations on a hybrid unstructured mesh. An approximate evaluation technique for the residual term at a new time level is presented according to the analysis of the main physical mechanism introduced by the lower-upper symmetric Gauss-Seidel (LU-SGS) relaxation-based backward Euler implicit method. The residual evaluation method is computationally inexpensive because it does not require flux calculations for every cell surface. The approximated new time residual can be obtained without considerable computational effort; thus, a point-implicit scheme with a multigrid property is designed to march a further time step after the previous LU-SGS-based backward Euler stage. This step leads to the principal ingredient of the presented two-stage hybrid implicit scheme.To investigate the convergence behavior and performance of the two-stage hybrid implicit scheme, 2D and 3D viscous flows around the NACA0012 airfoil, NHLP 2D multi-airfoil, and DLR-F6 wingbody-pylon-nacelle configuration are simulated by using different grid types. The convergence histories of the single LU-SGS-based backward Euler scheme and the presented two-stage hybrid implicit scheme are analyzed and compared for each test case. The test results show that the hybrid implicit scheme is more efficient and robust than the single-stage LU-SGS scheme.

“…Moreover, the ALE rezoning and remapping steps are computationally expensive and additional treatments in removing or limiting them can effectively enhance the efficiency of a standard ALE approach. For example, Zhang et al [8,9] developed a dynamic hybrid grid approach to improve their mesh with minimal local rezoning and remapping requirements. They used the spring-analogy method to deform their triangular meshes.…”

mentioning

confidence: 99%

“…Both of these shapes can simultaneously appear in a hybrid mesh [18]. In the flow fields with moving boundary or deformable mesh, the use of a hybrid mesh is very advantageous [8,9]. First, it uses the flexibility of unstructured triangular…”

mentioning

confidence: 99%

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

Naderi

Darbandi

Taeibi-Rahni

2009

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.