International Journal for Numerical Methods in Fluids

Chen, Yong; Zhu, Hanhua

doi: 10.1002/fld.5195pmid: N/A

A one‐point second‐order Dirichlet boundary condition for convection‐diffusion equation based on the lattice Boltzmann method has been proposed. The unknown temperature distribution is interpolated from the distributions at the wall node and fluid node nearest to the wall in the direction of the lattice velocity. At the wall node, the unknown temperature distribution is expressed as a summation of equilibrium and nonequilibrium distributions. The equilibrium distribution is obtained using the wall temperature, while the nonequilibrium distribution is approximated from the nearest fluid node in the direction of the lattice velocity. Both asymptotic analysis and numerical simulations of heat conduction indicate that the Dirichlet boundary condition is second‐order accurate. Further comparisons demonstrate that the newly proposed boundary method is sufficiently accurate to simulate natural convection, convective and unsteady heat transfer involving straight and curved boundaries.

Jalali Khouzani, H.; Kamali‐Moghadam, R.

doi: 10.1002/fld.5192pmid: N/A

A new optimization techniques based on the adjoint lattice Boltzmann method is derived for airfoil inverse design in laminar compressible flows. In this study, the developed adjoint lattice Boltzmann scheme based on the circular function (CF) is extended for airfoil inverse design problems in laminar incompressible and compressible flows. New mathematical derivation based on compressible lattice Boltzmann equations (LBE) is developed which can find target shape of an airfoil with available desired pressure distribution. The adjoint lattice Boltzmann method is extended for both the incompressible and compressible flows by selecting the circular function idea for calculating the equilibrium distribution functions. So, the adjoint equation is also expanded based on CF idea for calculation of objective function gradient vector. The steepest decent technique is utilized as gradient optimizer. Also, a novel solution is presented to remove singularity problem of the adjoint boundary condition. In order to validate the developed optimization algorithm, results are presented for both incompressible and compressible inverse problem in steady and unsteady flow and accurate results are obtained.

doi: 10.1002/fld.5111pmid: N/A

Stock, Antoine; Lartigue, Ghislain; Moureau, Vincent

doi: 10.1002/fld.5191pmid: N/A

In the context of unsteady 3D simulations of particle‐laden flows, a new double‐constraint load balancing strategy for Euler–Lagrange models is proposed. The method relies on an existing Eulerian partitioning and implements a Lagrangian load balancing step, which is orthogonal to the pre‐existing Eulerian balancing. This orthogonality property ensures to keep a near‐to‐ideal Eulerian load balance while strongly improving the distribution of the Lagrangian particles on the processors. The method has been designed to handle large unstructured 3D meshes on complex geometries. Lagrangian performance measurements performed on massively parallel simulations of realistic spray cases show a CPU cost reduction up to 70% compared to the unbalanced case.

Cao, Can; Gui, Nan; Zhang, Xiaoxi; Huang, Xiaoli; Yang, Xingtuan; Tu, Jiyuan; Jiang, Shengyao

doi: 10.1002/fld.5194pmid: N/A

A diffusion‐equation‐based kernel function (called the diffusive kernel) is proposed for flow and heat transfer simulation by the smoothed‐particle‐hydrodynamics (SPH) method. This new diffusive function has basic features of physics‐based, intrinsically conservative, and mathematically smoothing, because of a general solution of the diffusion equation. Three cases have been employed for method validation. One is the SOD's problem (a one‐dimensional case of the Riemann problem). The SPH simulation with the new kernel is compared to both analytical solutions and the SPH simulation by the third‐order B‐spline kernel. The second one is the dam‐break case to compare the performance of the cubic‐spline kernel, the quintic‐spline kernel, and the Wendland C2 kernel with the current diffusive kernel. The present kernel seems to perform as well as the well‐known Wendland C2 and the quintic kernels. The last case is natural convection in a concentric circular domain with temperature differences between the inner and outer concentric walls. Both the Gaussian kernel and the diffusive kernel were used for comparison and validation. Good consistency between numerical and analytical results, as well as experimental results, validates the good performance of the current diffusive kernel. After validation, it is clear that the diffusive kernel can simulate both the shock wave and natural convective heat transfer very well, and is much better than the conventional Gaussian kernel except for computational efficiency. The kernel profiles, together with their derivatives and integrals, are explored to explain why the diffusive kernel's performance is much better. Finally, to increase numerical efficiency, a fitted expression of the diffusive kernel is also given. The fitted diffusive kernel can reach the same level of computational efficiency as the Gaussian kernel while maintaining the basic advantages of the current diffusive kernel, which gives a choice for practical application.

He, L.

doi: 10.1002/fld.5190pmid: N/A

The primary challenges for simulating a turbulent flow over a micro‐structured surface arise from the two hugely disparate spatial length scales. For fluid–solid coupled conjugate heat transfer (CHT), there is also a time‐scale disparity. The present work addresses the scale disparities based on a two‐scale framework. For the spatial scale disparity, a dual meshing is employed to couple a global coarse‐mesh domain with local fine‐mesh blocks around micro‐structures through source terms generated from the local fine‐mesh and propagated to the global coarse‐mesh domain. The convergence and robustness of the source terms driven coarse‐mesh solution is enhanced by a balanced eddy‐viscosity damping. In this work, the two‐scale method previously developed only for a fluid‐domain is extended to a solid domain so that thermal conduction around micro‐elements can now be resolved accurately and efficiently. The fluid–solid timescale disparity is dealt with by a frequency domain approach. The time‐averaged (zeroth harmonic) is effectively obtained in the same way as steady CHT. And remarkably, wall temperature unsteadiness can be simply obtained from the fluid temperature harmonics through a wall fluid–solid temperature harmonic transfer‐function at minimal computational cost. The developed CHT capability is validated for an experimental internal cooling channel with multiple surface rib‐elements. For a test configuration with 100 micro‐structures, the fluid domain‐only, the solid domain‐only and the fluid–solid coupled CHT solutions are analyzed respectively to examine and demonstrate the validity of the present framework and implementation methods. Some of the results also serve to illustrate the primary underlying working of the methodology.

Wu, Wenbin; Liu, Na; Huang, Chao; Zhang, Pan; Liu, Moubin

doi: 10.1002/fld.5193pmid: N/A

In this study, a new cell‐centered Lagrangian discontinuous Galerkin (DG) scheme is presented to simulate gas‐water compressible flows. The two‐phase flows are governed by the compressible Euler equation with ideal and stiffened gas equations of state. We integrate the Lagrangian DG scheme with the exact gas‐water Riemann solver for calculating the numerical fluxes so that the inherent stiff features of gas‐water compressible flows are well addressed. Furthermore, in order to guarantee the positivity of the density and internal energy during the high Mach number calculation, the positivity‐preserving limiter and strong stability preserving temporal integral are incorporated to ensure the numerical stability. Six numerical examples are tested to show the accuracy, robustness and positivity‐preserving property of the present scheme. It can be found that the present scheme can handle challenging numerical cases involving large density ratio (up to 1000) and strong shock. The results obtained with the typical HLLC flux are also given for comparison and the present scheme with the exact Riemann solver shows higher accuracy, particularly in the presence of large density ratio at the gas‐water interface.

Gatti, Federico; Fois, Marco; Falco, Carlo; Perotto, Simona; Formaggia, Luca

doi: 10.1002/fld.5186pmid: N/A

We propose a highly scalable solver for a two‐dimensional depth‐integrated fluid dynamic model in order to simulate flow‐like landslides, such as debris or mud flows. The governing equations are discretized on quadtree meshes by means of a two‐step second‐order Taylor–Galerkin scheme, enriched by a suitable flux correction in order to avoid spurious oscillations, in particular near discontinuities and close to the wetting‐drying interface. A mesh adaptation procedure based on a gradient‐recovery a posteriori error estimator allows us to efficiently deal with a discretization of the domain customized to the phenomenon under investigation. Moreover, we resort to an adaptive scheme also in time to prevent filtering out the landslide dynamics, and to an interface tracking algorithm to avoid an excessive refinement in noninterfacial regions while preserving details along the wetting‐drying front. Finally, after verifying the performance of the proposed numerical method on idealized settings, we carry out a scalability analysis of the code both on idealized and real scenarios, to check the efficiency of the overall implementation.