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Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): J. Docampo-Sánchez, G.B. Jacobs, X. Li, J.K. Ryan
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Shujiang Tang, Mingjun Li
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Lionel Gamet, Marco Scala, Johan Roenby, Henning Scheufler, Jean-Lou Pierson
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Yucang Ruan, Xinting Zhang, Baolin Tian, Zhiwei He
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Yujie Zhu, Xiangyu Hu
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Romain Biolchini, Guillaume Daviller, Christophe Bailly, Guillaume Bodard
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Ali Raeisi Isa-Abadi, Vincent Fontaine, Hamid-Reza Ghafouri, Anis Younes, Marwan Fahs
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Ahmad Shoja-Sani, Ehsan Roohi, Stefan Stefanov
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Jean-François Monier, Feng Gao, Jérôme Boudet, Liang Shao
Publication date: 15 December 2020
Source: Computers & Fluids, Volume 213
Author(s): Yan Song, Yan Liu, Xiong Zhang
In this article, we present a direction splitting method, combined with a nonlinear iteration, for the compressible Navier‐Stokes equations in spherical coordinates. The aim of this work was to develop a method that would work efficiently in the limit of very small to vanishing Mach numbers, and we demonstrate here, using a numerical example, that the method shows good convergence and stability at Mach numbers in the range [10−2, 10−6]. The algorithm is particularly suitable for a massive parallel implementation, and we show some results demonstrating its excellent weak scalability.
In this article, we present a direction splitting method, combined with a nonlinear iteration, for the compressible Navier‐Stokes equations in spherical coordinates. The method is aimed at solving the equations on the sphere, and can be used for a regional geophysical simulations as well as simulations on the entire sphere. The aim of this work was to develop a method that would work efficiently in the limit of very small to vanishing Mach numbers, and we demonstrate here, using a numerical example, that the method shows good convergence and stability at Mach numbers in the range [10−2, 10−6]. We also demonstrate the effect of some of the parameters of the model on the solution, on a common geophysical test case of a rising thermal bubble. The algorithm is particularly suitable for a massive parallel implementation, and we show below some results demonstrating its excellent weak scalability.
An improved r‐factor algorithm for TVD schemes is proposed to extend the TVD schemes to non‐uniform unstructured grids. The computational results show that the equation L UC /L CD = (L Cf /L fD ) is appropriate to determine the further upwind node U, comparing with Hou's method. After that, the inverse‐distance weighting average method is superior to the Gauss theory method to estimate the value of node U. Furthermore, the deviations between the value of cell centroids and of their corresponding auxiliary points need to be exploited. The numerical studies indicate that monotonous behavior and higher accuracy can be obtained by using the new algorithm, in comparison to Hou's r‐factor algorithm. Convection of a double‐step profile using Superbee scheme with coarse grids: (A) ϕ profile at y = 0.5, (B) ϕ profile at x = 0.75. Convection of a sinusoidal profile using Superbee scheme with coarse grids: (C) ϕ profile at y = 0.5, (D) ϕ profile at x = 0.75.
For advection simulation, an improved r‐factor algorithm for total variational diminishing (TVD) schemes is proposed to extend the TVD schemes to non‐uniform unstructured grids. In the new algorithm, the further upwind node (called node U) location is modified based on the size differences of the related grids, that is, the formula of the relationship between two length ratios, L UC /L CD = L Cf /L fD , should be maintained to reveal the meaning of r‐factor correctly on non‐uniform unstructured grids. After that, the inverse‐distance weighting average method rather than the Gauss theory method is adopted to estimate the value of node U. Furthermore, the deviations between the value of cell centroids and of their corresponding auxiliary points are exploited to complete the algorithm. The new algorithm is utilized in two pure convection cases, including a double‐step profile and a sinusoidal profile. The algorithm was compared against the Hou's r‐factor algorithm by using Superbee and Van Leer limiters on two‐dimension non‐uniform unstructured grids. The results indicate that a monotonous behavior and a higher accuracy result can be obtained by using the new algorithm.
We proposes a new corner boundary condition for the DUGKS, which is deduced strictly in theory and available to satisfy conservation relations. The new corner boundary condition is validated by three numerical tests: the flow past a square cylinder (external flow), lid‐driven cavity flow (internal flow) and flow past the AUV (non right angle corner). The results show that the convergence efficiency and accuracy of the DUGKS are improved by the new method.
The implementation of the boundary condition at the corner points is very important. The discontinuities at the corner points propagate in the computational domain and have a great impact on the surrounding points and the global solution in the evolution process, resulting in the poor precision or the unphysical oscillatory behavior. However, it had been a largely under explored domain in the discrete unified gas kinetic scheme (DUGKS) methods. In the last few years, the DUGKS is proposed as a mesoscopic finite volume method with great development potential. In order to improve accuracy and efficiency, this paper proposes a new corner boundary condition for the DUGKS, which is deduced strictly in theory and available to satisfy conservation relations. The new corner boundary condition is validated by three numerical tests: the flow past a square cylinder (external flow), lid‐driven cavity flow (internal flow) and flow past the AUV (nonright angle corner). The results show that the convergence efficiency and accuracy of the DUGKS are improved by the new corner boundary condition.
In this article, we propose first‐order and second‐order linear, unconditionally energy stable, splitting schemes for solving the magnetohydrodynamics (MHD) system. We transform a double saddle points problem into a set of elliptic type problems to solve the MHD system. We further prove that time semi‐discrete schemes and fully discrete schemes are unconditionally energy stable.
In this article, we propose first‐order and second‐order linear, unconditionally energy stable, splitting schemes for solving the magnetohydrodynamics (MHD) system. These schemes are based on the projection method for Navier–Stokes equations and implicit–explicit treatments for nonlinear coupling terms. We transform a double saddle points problem into a set of elliptic type problems to solve the MHD system. Our schemes are efficient, easy to implement, and stable. We further prove that time semidiscrete schemes and fully discrete schemes are unconditionally energy stable. Various numerical experiments, including Hartmann flow and lid‐driven cavity problems, are implemented to demonstrate the stability and the accuracy of our schemes.
This paper demonstrates the characteristics of interparticle forces and forcing schemes in pseudopotential lattice Boltzmann simulations. The Yuan‐Schaefer (YS), multipseudopotential interaction (MPI) and piecewise linear methods are examined as techniques of equation of state (EOS) inclusion in pseudopotential models. It is suggested here that it is important to have an understanding of the interparticle forces generated by the models in order to obtain good quality results. Poor choice of parameters can lead to generation of unphysical interactions. The piecewise linear method is found to perform well and to decouple parameters. It decouples the density ratio from the surface tension and from the collision operator relaxation rates. It is proposed that the decoupling occurs due to generation of lower values of high‐order error terms in the interfacial region by the piecewise linear EOS. In general, the multiple‐relaxation‐time (MRT) collision operator should be combined with the Huang‐Wu forcing scheme for simulating high values of surface tension and with the Li‐Luo method for simulating low values of surface tension. It is found that reducing kinematic viscosity is more detrimental to the stability of the simulations than increasing the density ratio. Introducing a kinematic viscosity ratio between the phases practically eliminates the influence of density ratio on spurious velocities. The factors affecting stability of dynamic simulations are examined. It is found that they have the following hierarchy from the greatest impact to the least: kinematic viscosity ratio between the phases; bulk viscosity; method of EOS inclusion and reduced temperature/ density ratio.
We analyze the accuracy properties of both first‐order upwind finite difference and vertex‐centered finite volume approximations for linear transport problems with nonzero divergence velocity field. Such upwind schemes are routinely used in established spectral wave models. We conclude that the finite difference scheme offers superior convergence rates over the finite volume scheme for nonsmooth velocities. Theoretical results are supported by numerical computations, whereas practical consequences for the simulation of wave shoaling and refraction over shoals are demonstrated.
We are concerned with the numerical solution of a linear transport problem with nonzero divergence velocity field that originates from the spectral energy balance equation describing the evolution of wind waves and swells in coastal seas. The discretization error of the commonly used first‐order upwind finite difference and first‐order vertex‐centered upwind finite volume schemes in one space dimension is analyzed. Smoothness of nondivergent velocity field plays a crucial role in this. No such analysis has been attempted to date for such problems. The two schemes studied differ in the manner in which they treat the scalar flux numerically. The finite difference variant is shock captured, whereas the vertex‐centered finite volume approximation employs an arithmetic mean of the velocity and appears not to be flux conservative. The methods are subsequently extended to two dimensions on triangular meshes. Numerical experiments are provided to verify the convergence analysis. The main finding is that the finite difference scheme displays optimal rates of convergence and offers higher accuracy over the finite volume scheme, regardless the regularity of the velocity field. The latter scheme notably yields convergence rates of 0.5 and 0 in L 2‐norm and L ∞ ‐norm, respectively, when the velocity field is not smooth. A test case illustrating wave shoaling and refraction over submerged shoals is also presented and demonstrates the practical importance of flux conservation.
A novel flux‐splitting method that can preserve the flux conservation properties for the steady shock waves is proposed in present paper. The proposed method is based on the total variation diminishing (TVD) scheme, and the dissipative flux term is constructed by the flux directly instead of conservative variables. Similar transformations are imposed on the anti‐dissipation term, which is formulated by utilizing the limiter function. Numerical experiments were performed on the one, quasi one and two dimensional shock wave problems. The computed results show that, the steady shock waves can be accurately captured within two grid points by the proposed conservative flux‐splitting (CFS) method, and numerical oscillations are successfully eliminated near the flow discontinuities. The conservation and accuracy of present method are demonstrated by comparisons with the TVD, flux vector splitting (FVS) and flux difference splitting (FDS) methods.
For the frequent task of computing pressure from given flow velocities, we devise the first variational formulation for the pressure Poisson equation that fully accounts for viscous effects, including non‐Newtonian behavior, and also allows for compressibility — while still enabling the use of standard Lagrangian finite element basis functions for all quantities of interest. Various numerical examples are provided to showcase the potential of this novel approach.
Computing pressure fields from given flow velocities is a task frequently arising in engineering, biomedical, and scientific computing applications. The so‐called pressure Poisson equation (PPE) derived from the balance of linear momentum provides an attractive framework for such a task. However, the PPE increases the regularity requirements on the pressure and velocity spaces, thereby imposing theoretical and practical challenges for its application. In order to stay within a Lagrangian finite element framework, it is common practice to completely neglect the influence of viscosity and compressibility when computing the pressure, which limits the practical applicability of the pressure Poisson method. In this context, we present a mixed finite element framework which enables the use of this popular technique with generalized Newtonian fluids and compressible flows, while allowing standard finite element spaces to be employed for the unknowns and the given data. This is attained through the use of appropriate vector calculus identities and simple projections of certain flow quantities. In the compressible case, the mixed formulation also includes an additional equation for retrieving the density field from the given velocities so that the pressure can be accurately determined. The potential of this new approach is showcased through numerical examples.
This work describes a detailed mathematical procedure in relation to a novel third‐order WENO scheme for the inviscid term of a system of nonlinear equations in the generalized grid system. The scheme developed minimizes the linear and nonlinear sources of dissipation error associated with the classical fifth‐order WENO scheme. The former is minimized by optimizing the resolving efficiency of the scheme whereas the latter is minimized by fixing the accuracy at the second‐order critical point via re‐defining the nonlinear weights. Moreover, the spectral property of second‐order viscous derivative, approximated by the single and double applications of the standard fourth‐order central finite difference scheme, is presented. The two‐dimensional Euler and Navier‐Stokes equations in the generalized grids are mainly pursued. For the robustness in terms of capturing discontinuous and smooth structures, particularly two problems, which are difficult to handle in Cartesian grids, are chosen for discussion. The first one deals with a supersonic shock hitting the circular cylinder and generating all the possible flow inconsistencies. The other one deals with a subsonic flow over a circular cylinder at the incompressible limit. The numerical results are found to be in good agreement with the experimental data.
The moving discontinuous Galerkin finite element method with interface condition enforcement (MDG‐ICE) is applied to the case of viscous flows. This method uses a weak formulation that separately enforces the conservation law, constitutive law, and the corresponding interface conditions in order to provide the means to detect interfaces or under‐resolved flow features. To satisfy the resulting overdetermined weak formulation, the discrete domain geometry is introduced as a variable, so that the method implicitly fits a priori unknown interfaces and moves the grid to resolve sharp, but smooth, gradients, achieving a formof anisotropic curvilinear r‐adaptivity. This approach avoids introducing low‐order errors that arise using shock capturing, artificial dissipation, or limiting. The utility of this approach is demonstrated with its application to a series of test problems culminating with the compressible Navier‐Stokes solution to a Mach 5 viscous bow shock for a Reynolds number of 105 in two‐dimensional space. Time accurate solutions of unsteady problems are obtained via a space‐time formulation, in which the unsteady problem is formulated as a higher dimensional steady space‐time problem. The method is shown to accurately resolve and transport viscous structures without relying on numerical dissipation for stabilization.
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s): Jun Wang, Ehssan Nazockdast, Alex Barnett
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s): Martin Almquist, Eric M. Dunham
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s): L. Markeeva, I. Tsybulin, I. Oseledets
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s): Xi-Yuan Yin, Olivier Mercier, Badal Yadav, Kai Schneider, Jean-Christophe Nave
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s): Oriol Colomés, Alex Main, Léo Nouveau, Guglielmo Scovazzi
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s): Elena Bachini, Matthew W. Farthing, Mario Putti
Publication date: 1 January 2021
Source: Journal of Computational Physics, Volume 424
Author(s):
Publication date: Available online 25 November 2020
Source: Journal of Computational Physics
Author(s): Brody R. Bassett, J. Michael Owen, Thomas A. Brunner
Publication date: Available online 25 November 2020
Source: Journal of Computational Physics
Author(s): Brody R. Bassett, J. Michael Owen, Thomas A. Brunner
Publication date: Available online 25 November 2020
Source: Journal of Computational Physics
Author(s): T. Kadeethum, H.M. Nick, S. Lee, F. Ballarin
Effect of finite ion size on the transport of a neutral solute across the porous wall of a nanotube is presented in this study. Modified Poisson–Boltzmann equation without the Debye–Huckel approximation is used to determine the potential distribution within the tube. Power law fluid is selected for the study, as its rheology resembles closely to the real-life physiological fluids. The flow within the tube is actuated by the combined effects of pressure and electroosmotic forces. Steady-state solute balance equation is solved by the similarity technique in order to track the solute transport across the tube. The effects of ionic radius, ionic concentration, and flow behavioral index on the length-averaged Sherwood number, permeate flux, and permeate concentration are analyzed. This study will be extremely helpful in predicting the transport characteristics of a neutral solute in real physiological systems and also to fine-tune the performance of microfluidic devices having porous wall.
We carry out a priori tests of linear and nonlinear eddy viscosity models using direct numerical simulation (DNS) data of square duct flow up to friction Reynolds number \({\text {Re}}_\tau =1055\) . We focus on the ability of eddy viscosity models to reproduce the anisotropic Reynolds stress tensor components \(a_{ij}\) responsible for turbulent secondary flows, namely the normal stress \(a_{22}\) and the secondary shear stress \(a_{23}\) . A priori tests on constitutive relations for \(a_{ij}\) are performed using the tensor polynomial expansion of Pope (J Fluid Mech 72:331–340, 1975), whereby one tensor base corresponds to the linear eddy viscosity hypothesis and five bases return exact representation of \(a_{ij}\) . We show that the bases subset has an important effect on the accuracy of the stresses and the best results are obtained when using tensor bases which contain both the strain rate and the rotation rate. Models performance is quantified using the mean correlation coefficient with respect to DNS data \({\widetilde{C}}_{ij}\) , which shows that the linear eddy viscosity hypothesis always returns very accurate values of the primary shear stress \(a_{12}\) ( \({\widetilde{C}}_{12}>0.99\) ), whereas two bases are sufficient to achieve good accuracy of the normal stress and secondary shear stress ( \({\widetilde{C}}_{22}=0.911\) , \({\widetilde{C}}_{23}=0.743\) ). Unfortunately, RANS models rely on additional assumptions and a priori analysis carried out on popular models, including k– \(\varepsilon \) and \(v^2\) –f, reveals that none of them achieves ideal accuracy. The only model based on Pope’s expansion which approaches ideal performance is the quadratic correction of Spalart (Int J Heat Fluid Flow 21:252–263, 2000), which has similar accuracy to models using four or more tensor bases. Nevertheless, the best results are obtained when using the linear correction to the \(v^2\) –f model developed by Pecnik and Iaccarino (AIAA Paper 2008-3852, 2008), although this is not built on the canonical tensor polynomial as the other models.
The paper describes the longitudinal dispersion of passive tracer materials released into an incompressible viscous fluid, flowing through a channel with walls having first-order reaction. Its model is based on a steady advection–diffusion equation with Dirichlet’s and mixed boundary conditions, and whose solution represents the concentration of the tracers in different downstream stations. For imposing the boundary conditions properly, artanh transformation is used to convert the infinite solution space to a finite one. A finite difference implicit scheme is used to solve the advection–diffusion equation in the computational region, and an inverse transformation is employed for the solution in the physical region. It is shown how the mixing of the tracer molecule influenced by the shear flow and due to the action of the absorption parameter at both the walls of the channel. For convection-dominated flow, uniform mesh is failed to capture the layer phenomena along the different downstream stations and a piecewise uniform mesh; namely, Shishkin mesh is used. The results are compared with existing experimental and numerical data available in the literature, and we have achieved an excellent agreement with them. The study plays a significant role to understand the basic mechanisms of sewage dispersion.
In this study, we propose a novel computational model for simulating the coffee-ring phenomenon. The proposed method is based on a phase-field model and Monte Carlo simulation. We use the Allen–Cahn equation with a pinning boundary condition to model a drying droplet. The coffee particles inside the droplet move according to a random walk function with a truncated standard normal distribution under gravitational force. We perform both two-dimensional and three-dimensional computational experiments to demonstrate the accurate simulation of the coffee-ring phenomenon by the proposed model.
Oscillatory instability of buoyancy convection in a laterally heated cube with perfectly thermally conducting horizontal boundaries is studied. The effect of the spanwise boundaries on the oscillatory instability onset is examined. The problem is treated by Krylov-subspace-iteration-based Newton and Arnoldi methods. The Krylov basis vectors are calculated by a novel approach that involves the SIMPLE iteration and a projection onto a space of functions satisfying all linearized and homogeneous boundary conditions. The finite volume grid is gradually refined from \(100^{3}\) to \(256^{3}\) finite volumes. A self-sustaining oscillatory process responsible for the instability onset is revealed, visualized and explained.
The mixing in three-dimensional enclosures is investigated numerically using flow in cubical cavity as a geometrically simple model of various natural and engineering flows. The mixing rate is evaluated for up to the value of Reynolds number \(\hbox {Re}=2000\) for several representative scenarios of moving cavity walls: perpendicular motion of the parallel cavity walls, motion of a wall in its plane along its diagonal, motion of two perpendicular walls outward the common edge, and the parallel cavity walls in motion either in parallel directions or in opposite directions. The mixing rates are compared to the well-known benchmark case in which one cavity wall moves along its edge. The intensity of mixing for the considered cases was evaluated for (i) mixing in developing cavity flow initially at rest, which is started by the impulsive motion of cavity wall(s), and (ii) mixing in the developed cavity flow. For both cases, the initial interface of the two mixing fluids is a horizontal plane located at the middle of the cavity. The mixing rates are ranked from fastest to slowest for twenty time units of flow mixing. The pure convection mixing is modeled as a limit case to reveal convective mechanism of mixing. Mixing of fluids with different densities is modeled to show the advantage in terms of mixing rate of genuinely 3D cases. Grid convergence study and comparison with published numerical solutions for 3D and 2D cavity flows are presented. The effects of three-dimensionality of cavity flow on the mixing rate are discussed.
This work deals with the characterization of the closed-loop control performance aiming at the delay of transition. We focus on convective wavepackets, typical of the initial stages of transition to turbulence, starting with the linearized Kuramoto–Sivashinsky equation as a model problem representative of the transitional 2D boundary layer; its simplified structure and reduced order provide a manageable framework for the study of fundamental concepts involving the control of linear wavepackets. The characterization is then extended to the 2D Blasius boundary layer. The objective of this study is to explore how the sensor–actuator placement affects the optimal control problem, formulated using linear quadratic Gaussian (LQG) regulators. This is carried out by evaluating errors of the optimal estimator at positions where control gains are significant, through a proposed metric, labelled as \(\gamma \) . Results show, in quantitative manner, why some choices of sensor–actuator placement are more effective than others for flow control: good (respectively, bad) closed-loop performance is obtained when estimation errors are low (respectively, high) in the regions with significant gains in the full-state-feedback problem. Unsatisfactory performance is further understood as dominant estimation error modes that overlap spatially with control gains, which shows directions for improvement of a given set-up by moving sensors or actuators. The proposed metric and analysis explain most trends in closed-loop performance as a function of sensor and actuator position, obtained for the model problem and for the 2D Blasius boundary layer. The spatial characterization of the \(\gamma \) -metric provides thus a valuable and intuitive tool for the problem of sensor–actuator placement, targeting here transition delay but possibly extending to other amplifier-type flows.
We present a comprehensive analysis of the cumulant lattice Boltzmann model with the three-dimensional Taylor–Green vortex benchmark at Reynolds number 1600. The cumulant model is investigated in several different variants, using regularization, fourth-order convergent diffusion and fourth-order convergent advection with and without limiters. In addition, a cumulant model combined with a WALE sub-grid scale model is being evaluated. The turbulence model is found to filter out the high wave number contributions from the energy spectrum and the enstrophy, while the non-filtered cumulant methods show good correspondence to spectral simulations even for the high wave numbers. The application of the WALE turbulence model appears to be counter productive for the Taylor–Green vortex at a Reynolds number of 1600. At much higher Reynolds numbers ( \({\hbox {Re}}=160{,}000\) ) a deviation from the ideal Kolmogorov theory can be observed in the absence of an explicit turbulence model. Cumulant models with fourth-order convergent diffusion show much better results than single relaxation time methods.
Purpose: We present a constructive procedure for the calculation of 2-D potential flows in periodic domains with multiple boundaries per period window.
Methods: The solution requires two steps: (i) a conformal mapping from a canonical circular domain to the physical target domain, and (ii) the construction of the complex potential inside the circular domain. All singly periodic domains may be classified into three distinct types: unbounded in two directions, unbounded in one direction, and bounded. In each case, we use conformal mappings to relate the target periodic domain to a canonical circular domain with an appropriate branch structure.
Results: We then present solutions for a range of potential flow phenomena including flow singularities, moving boundaries, uniform flows, straining flows and circulatory flows.
Conclusion: By using the transcendental Schottky-Klein prime function, the ensuing solutions are valid for an arbitrary number of obstacles per period window. Moreover, our solutions are exact and do not require any asymptotic approximations.
The problem of the boundary condition setting is considered for creeping flows over cylindrical and spherical obstacles. The interaction of Newtonian and micropolar liquid with the solid surface is discussed in the context of the Stokes paradox and the cell model technique. Mathematical and mechanical aspects of various types of boundary conditions at the hypothetical liquid surface are considered in the framework of the spherical cell model used for the simulation of membrane flows. New properties of the flow pattern in a spherical cell are found, and their independence of the boundary conditions is rigorously proved. The criteria of the boundary conditions equivalence are derived in terms of the membrane porosity and hydrodynamic permeability.
