International Journal for Numerical Methods in Fluids最新文献

The numerical study of flow around a pair of spheres and a square array of spheres is investigated by using a direct-forcing immersed boundary method. Using high resolution three-dimensional computations, we analyzed the flow around several configurations: a sphere, a pair of spheres in a tandem arrangement with center-to-center streamwise ratio L/D ranging from 1 to 6, and a square array with 9 spheres in a uniform arrangement. In the latter case, we explore the ratio of array diameter (D_G) to sphere diameter (D) at 4, 5, 6 and 7. The center-to-center streamwise and transverse pitch is the same, varied from L/D = 1.5, 2, 2.5 to 3, and they were arranged in a square periodic array to allow uniform distribution within the array. Based on the effective direct-forcing immersed boundary projection method, the fractional time marching methodology is applied for solving four field variables involving three velocities and one pressure component. The pressure Poisson equation is advanced in space by using the fast Fourier transform (FFT) and a tridiagonal matrix algorithm (TDMA), effectively solving for the diagonally dominant tridiagonal matrix equations. A direct-forcing immersed boundary method is involved to treat the interfacial terms by adding the appropriate sources as force function at the boundary, separating the phases. Geometries featuring the stationary solid obstacles in the flow are embedded in the Cartesian grid with special discretizations near the embedded boundary using a discrete Dirac delta function to ensure the accuracy of the solution in the cut cells. An important characteristic of flow over the multiple spheres is devised by comparing with the drag and lift coefficients, as well as vortex shedding.

Granular flow problems characterized by large deformations are widespread in various applications, including coastal and geotechnical engineering. The paper deals with the application of a rigid-perfectly plastic two-phase model extended by the Drucker–Prager yield criterion to simulate granular media with a finite volume flow solver (FV). The model refers to the combination of a Bingham fluid and an Eulerian strain measure to assess the failure region of granular dam slides. A monolithic volume-of-fluid (VoF) method is used to distinguish between the air and granular phases, both governed by the incompressible Navier–Stokes equations. The numerical framework enables modeling of large displacements and arbitrary shapes for large-scale applications. The displayed validation and verification focuses on the rigid-perfectly plastic material model for noncohesive and cohesive materials with varying angles of repose. Results indicate a good agreement of the predicted soil surface and strain results with experimental and numerical data.

The classical staggered $��{�\mathbb{P}�}_{�N�}�-�{�\mathbb{P}�}_{�N�-�2�}�$ spectral element method (SEM) is revisited and extended to quasi-static magnetohydrodynamic (MHD) flows. In this realm, which is valid in the limit of vanishing magnetic Reynolds number, the evaluation of the Lorentz force in the momentum equation requires the electric current density, governed by Ohm's law and a charge conservation condition derived from Ampère's law, to be determined. Once discretized with the SEM, this translates into solving one additional problem for the electric potential involving the so-called consistent Poisson operator. The method is well suited for fully three-dimensional flows in complex geometries. Changes in resolution requirements aside, consideration of the electromagnetic quantities is estimated to increase the computational cost associated with MHD by about 40% relative to hydrodynamics. The accuracy and the capabilities of the scheme is demonstrated on a set of common flows from the MHD literature. Exponential convergence with polynomial order is confirmed for the electric current density.

A large Courant–Friedrichs–Lewy (CFL) algorithm is presented for the explicit, finite volume solution of hyperbolic systems of conservation laws, with a focus on the shallow water equations. The Riemann problems used in the flux computation are determined using averaging kernels that extend over several computational cells. The usual CFL stability constraint is replaced with a constraint involving the kernel support size. This makes the method unconditionally stable with respect to the size of the computational cells, allowing the computational mesh to be refined locally to an arbitrary degree without altering solution stability. The practical implementation of the method is detailed for the shallow water equations with topographical source term. Computational examples report applications of the method to the linear advection, Burgers and shallow water equations. In the case of sharp bottom discontinuities, the need for improved, well-balanced discretisations of the geometric source term is acknowledged.

The continuous adjoint method for transitional flows of compressible fluids is developed and assessed, for the first time in the literature. The gradient of aerodynamic objective functions (aerodynamic forces) with respect to design variables, in problems governed by the compressible Navier–Stokes equations coupled with the Spalart–Allmaras turbulence model and the $��\gamma ��-��\widetilde{�R�}�{�e�}_{�\theta �t�}�$ transition model (in three, non-smooth and smooth, variants of it), is computed based on the continuous adjoint method. The development of the adjoint to the smooth transition model variant proved to be beneficial. The accuracy of the computed sensitivity derivatives is verified against finite differences. Programming is performed in an in-house, vertex-centered finite-volume code, efficiently running on GPUs. The proposed continuous adjoint method is used in 2D and 3D aerodynamic shape optimization problems, namely the constrained optimization of the NLF(1)–0416 isolated airfoil and that of the ONERA M6 wing. The impact of “frozen transition” (assumption according to which the adjoint to the transition model equations are not solved) or “frozen turbulence” (by additionally ignoring the adjoint to the turbulence model) are evaluated; it is shown that both lead to inaccurate sensitivities.

We have presented a novel lattice Boltzmann approach for the non-uniform rectangular mesh based on the radial basis function approximation (RBF-LBM). The non-uniform rectangular mesh is a good option for local grid refinement, especially for the wall boundaries and flow areas with intensive change of flow quantities. Which allows, the total number of grid cells to be reduced and so the computational cost, therefore improving the computational efficiency. But the grid structure of the non-uniform rectangular mesh is no longer applicable to the classic lattice Boltzmann method (CLBM), which is based on the famous BGK collision-streaming evolution. This is why the present study is inspired by the idea of the interpolation-supplemented LBM (ISLBM) methodology. The ISLBM algorithm is improved in the present manuscript and developed into a novel LBM approach through the radial basis function approximation instead of the Lagrangian interpolation scheme. The new approach is validated for both steady states and unsteady periodic solutions. The comparison between the radial basis function approximation and the Lagrangian interpolation is discussed. It is found that the novel approach has a good performance on computational accuracy and efficiency. Proving that the non-uniform rectangular mesh allows grid refinement while obtaining precise flow predictions.

It is well known the Oseen iteration for the stationary Navier–Stokes equations is unconditionally stable. However, it is a coupled type scheme where the velocity $��u�$ and pressure $��p�$ are coupled together at each iteration. By treating pressure $��p�$ explicitly would lead to a decoupled iteration, but this treatment is unstable. In this article, we construct a decoupled and unconditionally stable iteration method to solve the stationary Navier–Stokes equations by adopting the pressure projection method to the temporal disturbed Navier–Stokes system whose solution approximates the steady state solution over time ($��t�\to �+�\infty �$). We also rigorously prove its unconditional stability. Numerical simulations demonstrate that our iterative method is more efficient and stable than the extensively used T-S and Oseen iterations, and could solve the fluid flow with high Reynolds number.

A modified fifth-order WENO-Z scheme is proposed by analogy with the non-normalized weights of the reformulated fifth-order adaptive order (AO) WENO scheme. We show that if the original fifth-order WENO-AO scheme is rewritten as the form of the conventional WENO combination, the resulting non-normalized weights can be divided into three parts: a constant one term, a local stencil smoothness measure term and a global stencil smoothness measure term. In order to make use of the latter two terms for constructing a modified WENO-Z scheme with enhanced performance, we change the form of the third term and introduce an adaptive scaling factor to adjust the contributions from the second and third terms. Numerical examples show that the modified fifth-order WENO-Z scheme has the advantage of high resolution in smooth regions and sharp capturing of discontinuities, and it can obtain evidently better results for shocked flows with small-scale structures compared with the recently developed WENO-Z+ and WENO-Z+M schemes.