International Jrnl For Numerical Methods in Fluids

doi: 10.1002/fld.5008pmid: N/A

Su, Xiaohui; Zhang, Kaixuan; Zhao, Yong; Zhang, Mingliang; Zhang, Jiantao

doi: 10.1002/fld.5102pmid: N/A

A novel dynamic adaptive unstructured mesh (DAUM) algorithm is proposed to solve incompressible multi‐object relative motion (MORM). The DAUM algorithm, consisting of exponential function deformation, adaptive edge swapping, and area Laplace smoothing, can greatly improve dynamic mesh robustness and perfectly overcome mesh skewness. The core of DAUM is the adaptive edge swapping inspired by Delaunay triangulation, which is distinguished from traditional edge swapping. The adaptive edge swapping can fully consider the relationship of neighbor elements only using Delaunay triangulation. Meanwhile, the implementation and reliability of adaptive edge swapping are better than the traditional edge swapping method due to eliminating the interference of the non‐convex polygon, so more code remedies can be avoided. Using the DAUM, none of the vertices is inserted or deleted so that the manipulation of the dynamic mesh is easily implemented and maintains computational efficiency in the process of mesh motion. Three representative geometries are used to assess the performance of the DAUM in MORM. To systematically analyze the advantages of DAUM, two relatively moving cylinders have been numerically investigated in incompressible flow. The inline force and lift force profiles on two cylinders are obtained and analyzed by using the flow field information. Three interaction stages are divided based on the parameter G and the interactional intensity of two inner anticlockwise vortices is considered as the division criteria. At the running process of the DAUM algorithm, the dynamic mesh quality is well controlled and remains in the high‐quality range based on the aspect ratio (AR) criterion. The results indicate that the proposed DAUM algorithm can properly solve the difficulties caused by MORM, especially for period oscillation motion.

Khamlich, Moaad; Pichi, Federico; Rozza, Gianluigi

doi: 10.1002/fld.5118pmid: 36248246

This work explores the development and the analysis of an efficient reduced order model for the study of a bifurcating phenomenon, known as the Coandă effect, in a multi‐physics setting involving fluid and solid media. Taking into consideration a fluid‐structure interaction problem, we aim at generalizing previous works towards a more reliable description of the physics involved. In particular, we provide several insights on how the introduction of an elastic structure influences the bifurcating behavior. We have addressed the computational burden by developing a reduced order branch‐wise algorithm based on a monolithic proper orthogonal decomposition. We compared different constitutive relations for the solid, and we observed that a nonlinear hyper‐elastic law delays the bifurcation w.r.t. the standard model, while the same effect is even magnified when considering linear elastic solid.

He, Zhiwei; Li, Li; Tian, Baolin

doi: 10.1002/fld.5119pmid: N/A

Nonlinear limiters are used to obtain the non‐oscillation property in the process of remapping physical quantities (mapping the physical quantities from the old grid to the new grid), which is an important step in the single/multimaterial arbitrary Lagrangian–Eulerian method. However, this operation introduces large numerical dissipation, causing severely smeared physical discontinuities and distortion of the physical quantities. Therefore, the design of an effective limiter that has less numerical dissipation and preserves the sharpness of discontinuous solutions is an area of interest. In this article, we apply the steepness‐adjustable harmonic (SAH) limiter (containing a steepness parameter) to the overlay‐intersection‐based remapping trying to obtain this goal. First, we analyze the construction process of the Barth–Jespersen (BJ) limiter and find a general methodology to modify it with different functions with symmetry property in the existing total‐variation‐diminishing limiters. Second, we investigate the possibility of other functions that do not possess the symmetry property and find an approximate technique to utilize the SAH limiter (which also does not possess the symmetry property) in the general methodology. Third, we propose a multidimensional method to adaptively calculate the steepness parameter of a whole mesh cell. With these steps, we propose a self‐adjusting steepness‐based limiter, which is further applied to the over‐intersection‐based remapping framework. The limiter is then verified by several remapping tests. The numerical results demonstrate a significant improvement in the resolution of discontinuities and the preservation of nominal second‐order accuracy for smooth structures. However, the bound‐preserving property is inevitably broken owing to the asymmetry of the SAH limiter, and additional techniques should be used to enforce the bounds of the algorithm.

Tavakoli Tameh, Mahboubeh; Shakeri, Fatemeh

doi: 10.1002/fld.5120pmid: N/A

We present a robust and effective method for the numerical solution of the biharmonic interface problem with discontinuities in both the solution and its derivatives. We use a mixed scheme, in which the biharmonic equation is decoupled to two Poisson equations. The proposed approach is based on the method of difference potentials combined with finite difference schemes on regular structured grid to solve this problem with high‐order accuracy on nonconforming domains. Representative numerical experiments confirm the accuracy and effectiveness of the proposed method and its ability to handle problems with coupled equations.

Toro, Eleuterio F.; Castro, Cristòbal E.; Vanzo, Davide; Siviglia, Annunziato

doi: 10.1002/fld.5099pmid: N/A

We present a flux vector splitting method for the one and two‐dimensional shallow water equations following the approach first proposed by Toro and Vázquez for the compressible Euler equations. The resulting first‐order schemes turn out to be exceedingly simple, with accuracy and robustness comparable to that of the sophisticated Godunov upwind method used in conjunction with complete non‐linear Riemann solvers. The technique splits the full system into two subsystems, namely an advection system and a pressure system. The sought numerical flux results from fluxes for each of the subsystems. As to the source terms, there is potential for treating general source terms by incorporating them into either subsystem. In this article we show preliminary results for the case of a discontinuous bottom, incorporated into the pressure system. Results show that the resulting method is well balanced. The basic methodology, extended on 2D unstructured meshes, constitutes the building block for the construction of numerical schemes of very high order of accuracy following the ADER approach. The presented numerical schemes are systematically assessed on a carefully selected suite of test problems with reference solutions, in one and two space dimensions. The applicability of the schemes is illustrated through simulations of tsunami wave propagation in the Pacific Ocean.

Vafakos, Georgios P.; Kafkas, Angelos; Papadopoulos, Polycarpos K.

doi: 10.1002/fld.5117pmid: N/A

In the present work, we present a new version of the pressure‐based implicit potential (IPOT) method for incompressible flows, which can be applied on a fully collocated mesh. The new version combines the IPOT algorithm with the Rhie and Chow (RC) technique, to produce solutions on collocated grids that are free of spurious pressure modes. The IPOT‐RC method retains all the benefits of the original algorithm, i.e. explicit velocity–pressure coupling, easy implementation and reduced iteration time, without requiring a special grid topology. The presentation of the IPOT‐RC method is accompanied by an extensive discussion on the cause of the spurious oscillations in zero‐div problems in general, and a possible cure that is linked to the RC technique. The IPOT‐RC method is validated through several benchmark problems including the lid‐driven cavity flow, flow over a backward facing step and direct numerical simulation of turbulent channel flow.

Mrad, Arwa; Caboussat, Alexandre; Picasso, Marco

doi: 10.1002/fld.5122pmid: N/A

We present a numerical model for the simulation of 3D sediment transport in a Newtonian flow with free surfaces. The Navier–Stokes equations are coupled with the transport, deposition, and resuspension of the particle concentrations, and a volume‐of‐fluid approach to track the free surface between water and air. The numerical method relies on operator splitting to decouple advection and diffusion phenomena, and a two‐grid method. An appropriate combination of characteristics, finite volumes, and finite elements methods is advocated. The numerical model is validated through comparisons with numerical experiments, sediment flushing, shear flow erosion, and the formation of dunes.