International Journal for Numerical Methods in Fluids最新文献

In this study, the approximate results of the fractional Fokker–Planck equations have been investigated. First, finite element schemes have been obtained using collocation finite element method based on the trigonometric quintic B-spline basis functions. Then, the present method is tested on two fundamental problems having appropriate initial conditions. The newly obtained numerical results contained the error norms $��L_2�$ and $��L_{\infty }�$ for various temporal and spatial steps are compared with the exact ones and other solutions. More accurate results have been obtained for large numbers of spatial and temporal elements.

A high-order discontinuous Galerkin (DG) method is presented for nonequilibrium multi-material ($��m�\ge �2�$) flow with sharp interfaces. Material interfaces are reconstructed using the algebraic THINC approach, resulting in a sharp interface resolution. The system assumes stiff velocity relaxation and pressure nonequilibrium. The presented DG method uses Dubiner's orthogonal basis functions on tetrahedral elements. This results in a unique combination of sharp multimaterial interfaces and high-order accurate solutions in smooth single-material regions. A novel shock indicator based on the interface conservation condition is introduced to mark regions with discontinuities. Slope limiting techniques are applied only in these regions so that nonphysical oscillations are eliminated while maintaining high-order accuracy in smooth regions. A local projection is applied on the limited solution to ensure discrete closure law preservation. The effectiveness of this novel limiting strategy is demonstrated for complex three-dimensional multi-material problems, where robustness of the method is critical. The presented numerical problems demonstrate that more accurate and efficient multi-material solutions can be obtained by the DG method, as compared to second-order finite volume methods.

The simulation of viscoelastic liquids using the Lattice–Boltzmann method (LBM) in full three dimensions remains a formidable numerical challenge. In particular the simulation of strongly shear-thinning fluids, where the ratio between the high-shear and low-shear viscosities is large, is often prevented by stability problems. Here we present a novel approach to overcome this issue. The central idea is to artificially increase the solvent viscosity which allows the method to benefit from the very good stability properties of the LBM. To compensate for this additional viscous stress, the polymer stress is reduced by the same amount. We apply this novel method to simulate two realistic cell carrier fluids, methyl cellulose and alginate solutions, of which the latter exhibits a viscosity ratio exceeding 10,000.

Based on three-dimensional seismic wave, simulations have become a pivotal aspect of seismic exploration. The diffusive-viscous wave equation, initially proposed by Goloshubin et al., is frequently utilized to describe seismic wave propagation in fluid-saturated media. However, obtaining numerical solutions for this equation has become an urgent issue in recent years. In this study, we present a cell-centered finite volume scheme utilizing a multipoint flux approximation that employs a “diamond stencil” on general polyhedral meshes to address the diffusive-viscous wave equation. Numerical tests exhibit that this new scheme attains optimal convergence, and its effectiveness is demonstrated through simulating vibrations induced by an earthquake source.

An original Immersed Boundary Method for solving moving body flows is proposed. This method couples (i) a Lagrangian Volume-of-Solid description of the solid object avoiding conservation issues and (ii) a robust implicit volume penalty forcing embedded in a low-Mach number projection method to account for the solid's impact on the fluid dynamics. A new composite velocity field is introduced to describe both solid and fluid domains in a single set of governing equations. The accuracy of the method has been assessed on several academic cases, involving stationary or moving bodies and with different mesh resolutions. The predicted forces on the solid are in excellent agreement with body-fitted reference cases. The system of equations is also proven to be fully mass conservative. Application of the method on a two-dimensional vertical axis turbine case shows a $��30�\%�$ reduction in computational cost compared to a body-fitted method.

We introduce semi-implicit Lagrangian Voronoi approximation (SILVA), a novel numerical method for the solution of the incompressible Euler and Navier–Stokes equations, which combines the efficiency of semi-implicit time marching schemes with the robustness of time-dependent Voronoi tessellations. In SILVA, the numerical solution is stored at particles, which move with the fluid velocity and also play the role of the generators of the computational mesh. The Voronoi mesh is rapidly regenerated at each time step, allowing large deformations with topology changes. As opposed to the reconnection-based Arbitrary-Lagrangian-Eulerian schemes, we need no remapping stage. A semi-implicit scheme is devised in the context of moving Voronoi meshes to project the velocity field onto a divergence-free manifold. We validate SILVA by illustrative benchmarks, including viscous, inviscid, and multi-phase flows. Compared to its closest competitor, the Incompressible Smoothed Particle Hydrodynamics method, SILVA offers a sparser stiffness matrix and facilitates the implementation of no-slip and free-slip boundary conditions.

The goal of this research is to propose a new modification of a non-equilibrium effect in the $��k�-�\omega �$ turbulence model to better predict high-speed turbulent flows. For that, the two local compressibility coefficients are included in the balance production/dissipation terms in a specific dissipation rate equation. The specific dissipation rate reacts to changes in the local Mach number and density through these local coefficients. The developed model is applied to the numerical simulation of the spatial supersonic turbulent airflow with round hydrogen injection. In that, the effects of the proposed turbulence model on the flow field behavior (shock wave and vortex formations, shock wave/boundary layer interaction, and mixture layer) are studied via the solution of three-dimensional Favre-averaged Navier–Stokes equations with a third-order Essentially Non-Oscillatory scheme. A series of numerical experiments are performed, in which an allowable range of local constants by comparing results with experimental data is obtained. The non-equilibrium modification by simultaneous decrease of the turbulence kinetic energy and increase of the specific dissipation rate gives a good agreement of the hydrogen depth penetration with experimental data. Also, the numerical experiment of the supersonic airflow with a nitrogen jet shows wall pressure distribution is consistent well with experimental data.