International Journal for Numerical Methods in Fluids

doi: 10.1002/fld.4860pmid: N/A

Li, Qiao‐Zhong; Lu, Zhi‐Liang; Zhou, Di; Niu, Xiao‐Dong; Guo, Tong‐Qin; Du, Bing‐Chen

doi: 10.1002/fld.4883pmid: N/A

Based on phase‐field theory, we develop a simple and robust single relaxation time (SRT) lattice Boltzmann (LB) model for simulating complex multiphase flows with large density ratios (up to 2000). The approach utilizes two LB equations (LBE), one is used to describe the interface behavior and the other is used to calculate the hydrodynamic properties. To improve the accuracy and stability in capturing interface, the high‐order LB model derived through the fourth‐order Chapman‐Enskog expansion analysis is applied to Cahn‐Hilliard equation. For solution of the flow field, a modified particle distribution function in the pressure‐velocity formulation is constructed to correctly consider the effect of local density variation and continuous pressure field. With such improvement, the proposed multiphase LB model is able to maintain numerical stability for the problem with very large density ratio, lower relaxation parameter and complex interface. For validation, a series of benchmark cases are carried out. Specially, the full potential of the proposed model is validated by bubble bursting at a free surface, bubble rising and droplet splashing with a density ratio of 2000. In all test cases, the obtained numerical results agree well with the reference data or the analytical solutions.

Li, Longxiang; Zhang, Qinghe

doi: 10.1002/fld.4884pmid: N/A

To develop a robust, well‐balanced and quadrature‐free Runge‐Kutta discontinuous Galerkin (RKDG) shallow water solver, we introduce an efficient wetting and drying (WD) treatment in this paper. The main feature of this WD treatment is the use of vertex‐based linear reconstructed solutions in transition (partially wet) regions and high‐order solutions in smooth wet areas. To preserve the positivity of water depth, we also propose a modified time step size with the quadrature‐free scheme. The advantages of the WD treatment include robustness and the capability to address arbitrary high‐order RKDG methods in wet regions, thus making the quadrature‐free scheme more accurate and applicable to various flooding and drying problems. Two numerical test cases are used to validate the numerical method, and the results indicate that the WD method is accurate and robust for different flow regimes with dry areas.

Sorokin, Konstantin E.; Perepechko, Yuri V.

doi: 10.1002/fld.4885pmid: N/A

This article presents the results of numerical analysis of acoustic impact generated by small finite source on heat and mass transfer of fluid‐saturated granular medium in a cavity heated from below. Thermodynamically consistent model of two‐phase medium is obtained by the method of conservation laws suggesting no equilibrium in pressure between the phases. The transition from diffusive to convective regime of heat and mass transfer in fluid‐saturated granular medium as a consequence of acoustic impact is shown. Effect of source frequency and initial flow pattern on the intensity of convective instability and configuration of dissipative structure is studied. Formation of stable and symmetric convective structure by choosing the source frequency is illustrated.

Liu, Xiaoxing; Morita, Koji; Zhang, Shuai

doi: 10.1002/fld.4886pmid: N/A

Particle methods have shown their potential for simulating multiphase flows due to the convenience in capturing interfaces. However, when it comes to estimate the surface tension, calculation of the curvature of the interface remains challenging. Traditional methods are based on derivative models to estimate the curvature analytically from the particle number density or color function that marks different phases. It is difficult to estimate the curvature accurately in traditional derivative models. In this study, background cells are built up and are used to predict the curvature through machine learning. By training on a data set generated using circles of varying sizes, a relation function is found to predict the curvature from the particle distribution near the interface. Together with the enhanced schemes developed in our previous study, multiphase flows with surface tension are studied within the framework of the moving particle semi‐implicit method.

Hernandez‐Duenas, Gerardo; Ramirez‐Santiago, Guillermo

doi: 10.1002/fld.4887pmid: N/A

In this work, we consider a hyperbolic one‐dimensional (1D) model for blood flow through compliant axisymmetric tilted vessels. The pressure is a function of the cross‐sectional area and other model parameters. Important features of the model are inherited at the discrete level by the numerical scheme. For instance, the existence of steady states may provide important information about the flow properties at low computational cost. Here, we characterize a large class of smooth equilibrium solutions by means of quantities that remain invariant. At the discrete level, the well‐balanced property in the numerical scheme leads to accurate results when steady states are perturbed. On the other hand, the model is equipped with an entropy function and an entropy inequality that can help us choose the physically relevant weak solutions. A large class of semidiscrete entropy‐satisfying numerical schemes is described. In addition, preservation of positivity for the cross‐sectional area is achieved. Numerical results show the scheme is robust, stable, and accurate. The ultimate goal of this article is the numerical application to cases that are more relevant from the medical viewpoint. In particular, a numerical simulation of cardiac cycles with appropriate parameters shows that increasing the rigidity of the artery walls delays the formation of shock waves. Gravity effects are also measured in tilted vessels, and a simulation using an idealized aorta model was conducted.

Ooi, Chinchun; Le, Quang Tuyen; Dao, My Ha; Nguyen, Van Bo; Nguyen, Hoang Huy; Ba, Te

doi: 10.1002/fld.4888pmid: N/A

In this work, we present the results obtained from integrating several machine learning (ML) models with projection‐based reduced order model for modeling the canonical case of flow past a stationary cylinder. We demonstrate how ML models can be used to model the time‐varying characteristics of the proper orthogonal decomposition (POD) coefficients, and that the locally interpolating models such as regression trees and k‐nearest neighbors seem to be better for such models than other models like support vector regression or long‐short term memory networks. In addition, our numerical experiments also show that these POD coefficients are most effectively modeled by using their own previous time values, as opposed to the inclusion of high energy POD modes. Last but not least, we demonstrate that these models, although trained on inlet velocities of 0.8, 1.0, and 1.2 m/s, can still predict the POD coefficients of flow fields for inlet velocities of 0.9 and 1.25 m/s, with root mean squared error of under 10%.

Zheng, Bo Xue; Sun, Lei; Chen, Zhen; Cheng, Cong; Liu, Chang Feng

doi: 10.1002/fld.4889pmid: N/A

In the present paper, an improved multiphase weakly compressible smoothed particle hydrodynamics model for balancing the accuracy and stability of the long‐term simulations is proposed to model the forced liquid sloshing in a tank. The governing equations of the multiphase flow are discretized by considering the density discontinuity over the interface. To suppress the pressure oscillation, a previous density correction term suitable only for single‐phase problems is modified and incorporated into the discrete continuity equation to suit multiphase problems. The modified density reinitialization algorithm is implemented to calculate the pressure of the boundary particles, and the coupled dynamic solid boundary treatment (SBT) is employed to determine the rigid wall condition. For convenience, a numerical probe algorithm is also proposed to accurately measure the wave height. The present model exhibits a better numerical stability than the previous multiphase smoothed particle hydrodynamics model, and its results well confirm with the experimental data of the forced sloshing of liquid excited by swaying or rolling.

Figueroa, Alejandro; Jackiewicz, Zdzisław; Löhner, Rainald

doi: 10.1002/fld.4890pmid: N/A

Computational fluid dynamics (CFD) has emerged as a successful tool for industry applications and basic science during the last decades. However, accurate solutions involving vortex propagation, and separated and turbulent flows, are still associated with high computing costs. In particular, large eddy simulations (LES) of complex geometries, such as a complete automobile, require several days on thousands of cores in order to obtain solutions with statistically relevant information. With an increase in the number of available cores, the number of degrees of freedom (DOF) per core can be reduced accordingly. When the number of DOF per core is below a certain threshold the total simulation time is not bounded by floating point operations (FLOPS), but by the time spend on communication between cores. To overcome this impediment we have identified and tested a class of two‐step Runge‐Kutta (TSRK) methods of high order with low number of stages, for time discretization of differential systems resulting from space discretization of weakly compressible Navier‐Stokes equations. These methods have not been used before in CFD simulations. The advantage of using these methods is reduction in communication times between cores. The numerical experiments indicate that the gains in computational performance of this new class of TSRK methods, as compared with classical Runge‐Kutta (RK) methods or low storage Runge‐Kutta (LSRK) schemes, are of the order of 25%, with no loss in accuracy.

Kassa, Abay Molla; Kumar, Kundan; Gasda, Sarah E.; Radu, Florin A.

doi: 10.1002/fld.4891pmid: N/A

In this article, we consider a nonlocal (in time) two‐phase flow model. The nonlocality is introduced through the wettability alteration induced dynamic capillary pressure function. We present a monotone fixed‐point iterative linearization scheme for the resulting nonstandard model. The scheme treats the dynamic capillary pressure functions semiimplicitly and introduces an L‐scheme type stabilization term in the pressure as well as the transport equations. We prove the convergence of the proposed scheme theoretically under physically acceptable assumptions, and verify the theoretical analysis with numerical simulations. The scheme is implemented and tested for a variety of reservoir heterogeneities in addition to the dynamic change of the capillary pressure function. The proposed scheme satisfies the predefined stopping criterion within a few number of iterations. We also compared the performance of the proposed scheme against the iterative implicit pressure explicit saturation scheme.