International Journal for Numerical Methods in Fluids最新文献

In this article, we study a mathematical model that represents the concentration polarization and osmosis effects in a reverse osmosis cross-flow channel with dense membranes at some of its boundaries. The fluid is modeled using the Navier–Stokes equations and the solution-diffusion is used to impose the momentum balance on the membrane. The scheme consist of a conforming finite element method with the velocity–pressure formulation for the Navier–Stokes equations, together with a primal scheme for the convection–diffusion equations. The Nitsche's method is used to impose the permeability condition across the membrane. Several numerical experiments are performed to show the robustness of the method. The resulting model accurately replicates the analytical models and predicts similar results to previous works. It is found that the submerged configuration has the highest permeate production, but also has the greatest pressure loss of all three configurations studied.

A piecewise circular interface construction (PCIC) method is described, where height functions based curvature estimates are directly utilised for accurate interface reconstruction under the framework of volume of fluid method. The present work is an attempt to develop a robust and accurate higher order interface reconstruction algorithm that is capable of accurate simulation of surface tension dominated flows. The proposed hybrid method (H-PCIC) is thus able to take advantage of merits of both PCIC and HF methods, achieving at least second order convergence with respect to both interface reconstruction and curvature computation. This is in addition to the significantly superior quality of the reconstructed interface with respect to PLIC methods. This seamless blending of the HF and PCIC quantities is enabled by c0-correction procedures applied to base PLIC and initial PCIC steps. More recent variants of the height function method with variable stencil size are used for calculation of radius of curvature. The capability of this proposed method towards simulation of flow problems within a well-balanced two-phase solver is established with help of multiple complex two-phase flow problems. This validation exercise also demonstrates the capability of PCIC class of methods towards solutions of two-phase flows with intricate physics.

The classical vorticity-streamfunction formulation (VSF) can avoid the difficulty in the calculation of pressure gradient term of the Navier Stokes equation via eliminating pressure gradient term from the theoretical basis. Within this context we propose a general VSF, together with redefined vorticity and streamfunction, so as to realize numerically stable and reliable simulations of binary fluids with an arbitrary density contrast. By incorporating the interface-tracking phase-field model based on the conservative Allen-Cahn equation [Phys. Rev. E 94, 023311 (2016)], the binary flow simulation framework is established. Numerical tests are conducted using the Lattice Boltzmann method (LBM), which is usually regarded as an easy-to-use tool for solving the Navier–Stokes equation but generally suffers from the drawback of not being capable of enforcing incompressibility. The LBM herein functions as a numerical tool for solving the vorticity transport equation, the streamfunction equation, and the conservative Allen-Cahn equation. Three two-dimensional benchmark cases, i.e., the Capillary wave, the Rayleigh–Taylor instability, and the droplet splashing on a thin liquid film, are discussed in detail to verify the present methodology. Results show good agreements with both analytical predictions and literature data, as well as good numerical stability in terms of high density ratio and high Reynolds number. Overall, the general VSF inherits the intrinsic superiority of the classical VSF in enforcing incompressibility, and offers a useful and reliable alternative for binary flow modeling.

Incomplete LU (ILU) smoothers are effective in the algebraic multigrid (AMG) $��V�$-cycle for reducing high-frequency components of the error. However, the requisite direct triangular solves are comparatively slow on GPUs. Previous work has demonstrated the advantages of Jacobi iteration as an alternative to direct solution of these systems. Depending on the threshold and fill-level parameters chosen, the factors can be highly nonnormal and Jacobi is unlikely to converge in a low number of iterations. We demonstrate that row scaling can reduce the departure from normality, allowing us to replace the inherently sequential solve with a rapidly converging Richardson iteration. There are several advantages beyond the lower compute time. Scaling is performed locally for a diagonal block of the global matrix because it is applied directly to the factor. Further, an ILUT Schur complement smoother maintains a constant GMRES iteration count as the number of MPI ranks increases, and thus parallel strong-scaling is improved. Our algorithms have been incorporated into hypre, and we demonstrate improved time to solution for linear systems arising in the Nalu-Wind and PeleLM pressure solvers. For large problem sizes, GMRES$��+�$AMG executes at least five times faster when using iterative triangular solves compared with direct solves on massively parallel GPUs.

The accurate capturing of shock waves by numerical methods has long been a focus of attention in engineering owing to singularity problems in discontinuities. In this article, a novel coupled Euler–Lagrange method (CELM) is proposed to capture shock waves and discontinuities with high resolution and high order of mapping accuracy. CELM arranges the Lagrange particles on an Euler grid to track the discontinuous points automatically, and the data pertaining to the grids and particles interact via a weighted mutual mapping method that not only achieves fourth-order accuracy in a smooth area of the solution but also maintains a steep discontinuous transition in the discontinuous area. In the virtual particle method, virtual particles are derived from the existing real particles; thus, the inflow and outflow of the particles and interpolation accuracy of the boundary are more easily realized. An accuracy test and energy convergence test demonstrated the fourth-order convergence accuracy and low energy dissipation of the CELM; the method exhibited lower error and better conservation ability than high-precision schemes such as WENO3 and WENO5. The Sod shock tube problem and Woodward–Colella problem showed higher discontinuity resolution of the CELM and ability to accurately track discontinuity points. Examples of Riemann problems were employed to prove that the CELM exhibits lower dissipation and higher shock resolution than WENO3 and WENO5. The CELM also showed an accurate structure based on particle distribution. Shockwave diffraction tests were conducted to prove that the CELM results showed good agreement with the experimental data and exhibited an accurate expansion wave. The CELM can also accurately simulate the collision of an expansion wave and vortex.

In flapping insect wings, veins support flexible wing membranes such that the wings form feathering and cambering motions passively from large elastic deformations. These motions are essentially important in unsteady aerodynamics of insect flapping flight. Hence, the underlying mechanism of this phenomenon is an important issue in studies on insect flight. Systematic parametric studies on strong coupling between a model wing describing these elastic deformations and the surrounding fluid, which is a direct formulation of this phenomenon, will be effective for solving this issue. The purpose of this study is to develop a robust numerical framework for these systematic parametric studies. The proposed framework consists of two novel numerical methods: (1) A fully parallelized solution method using both algebraic splitting and semi-implicit scheme for monolithic fluid–structure interaction (FSI) equation systems, which is numerically stable for a wide range of properties such as solid-to-fluid mass ratios and large body motions, and large elastic deformations. (2) A structural mechanics model for insect flapping wings using pixel modeling (pixel model wing), which is combined with explicit node-positioning to reduce computational costs significantly in controlling fluid meshes. The validity of the proposed framework is demonstrated for some benchmark problems and a dynamically scaled model incorporating actual insect data. Finally, from a parametric study for the pixel model wing flapped in fluid with a wide range of solid-to-fluid mass ratios, we find a FSI mechanism of feathering and cambering motions in flapping insect wings.

The study of multilayered shallow water equations has developed from a consideration of immiscible layers as a vertical mesh to the layer bounds as imaginary extremes for vertical integration of the flow equations. In the current work, a quasi three-dimensional flow model has been developed with the consideration of the spatiotemporal flexibility/variability of the pervious vertical discretization/layer ratios. Thus, in principle, vertical layering offers a nonuniform grid with a temporal variation. The system of equations thus formulated comprises a conservative part and the appended source/sink terms. These source/sink terms pertain to the inter-layer interactions such as mass/momenta transfer and interfacial stress, which have been treated in a novel implicit form alongwith the subgrid-scale eddy-viscosity for interlayer shear. They are integrated into the system through different physical considerations so as to arrive at a well-balanced numerical scheme in a regular finite volume grid. The model has been validated through the standard test-cases highlighting the conservation properties and the model's adaptability to uniform and nonuniform vertical meshes alongwith the spatiotemporal transitions of layer ratios, with a specific interest in limiting cases of wet/dry fronts. The increase in layer ratios tends to nearly replicate the full-scale model results in experimental scenarios at a lesser computational overhead.

A proper estimation of flow resistance coefficient of river is essential for precise simulations of river hydraulics. In addition to the cross-sectional geometry and hydraulic parameters, the alignment of the channel affects the flow resistance coefficient in case of meandering rivers. In the present study, a rigorous field study of 131 km along the Barak River was conducted to assess the influence of meandering on the flow resistance coefficient. The values of flow resistance co-efficient were calculated using Chezy and Manning's equations with measured field data and the values from both are compared. However, the variation in the flow resistance co-efficient along the channel calculated from Manning's equation is significantly less as it does not consider the undulation and meandering. Using these field data, an artificial neural network (ANN) model has been developed to predict the cross-sectional averaged flow resistance for meandering river. The model considered the influence of relative curvature, depth of flow, bed particle size, Froude number and Reynolds number including water temperature for accurate predictions of flow resistance coefficient. The ANN model was tested and validated using 237 field data sample. The values of the statistical parameters indicate a very good fit to the training dataset with coefficient of determination (R²) = 0.9566 for training and good fit for testing with R² = 0.8131. The developed ANN model has been compared with other model with the same data set to check its applicability.