An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

A flux splitting scheme is proposed for the general nonequilibrium flow equations with an aim at removing numerical dissipation of Van-Leer-type flux-vector splittings on a contact discontinuity. The scheme obtained is also recognized as an improved Advection Upwind Splitting Method (AUSM) where a slight numerical overshoot immediately behind the shock is eliminated. The proposed scheme has favorable properties: high-resolution for contact discontinuities; conservation of enthalpy for steady flows; numerical efficiency; applicability to chemically reacting flows. In fact, for a single contact discontinuity, even if it is moving, this scheme gives the numerical flux of the exact solution of the Riemann problem. Various numerical experiments including that of a thermo-chemical nonequilibrium flow were performed, which indicate no oscillation and robustness of the scheme for shock/expansion waves. A cure for carbuncle phenomenon is discussed as well.

A Flux Splitting Scheme with High-Resolution and Robustness for Discontinuities(Proceedings of the 12th NAL Symposium on Aircraft Computational Aerodynamics)

A unified gas-kinetic scheme for continuum and rarefied flows IV

应用DES(Detached-Eddy Simulation)方法数值模拟了3种不同失速类型的翼型的升力特性.DES方法结合了RANS(Reynolds-averaged Navier-Stokes)和LES(Large Eddy Simulation approaches)的优点.基于Spalart-Allmaras湍流模型,在近壁面DES体现为RANS模型的特点而在远离物面处又具有LES的亚格子模型的特性.对此模型使用了LU-SGS隐式格式求解.通过和实验结果对比,显示这种方法可以有效地预测翼型的失速特性.

Detached—Eddy Simulation方法模拟不同类型翼型的失速特性

Fuel cells and flow batteries are promising technologies to address climate change and air pollution problems. An understanding of the complex multiscale and multiphysics transport phenomena occurring in these electrochemical systems requires powerful numerical tools. Over the past decades, the lattice Boltzmann (LB) method has attracted broad interest in the computational fluid dynamics and the numerical heat transfer communities, primarily due to its kinetic nature making it appropriate for modeling complex multiphase transport phenomena. More importantly, the LB method fits well with parallel computing due to its locality feature, which is required for large-scale engineering applications. In this article, we review the LB method for gas–liquid two-phase flows, coupled fluid flow and mass transport in porous media, and particulate flows. Examples of applications are provided in fuel cells and flow batteries. Further developments of the LB method are also outlined.

Lattice Boltzmann modeling of transport phenomena in fuel cells and flow batteries

A unified gas kinetic scheme with moving mesh and velocity space adaptation

The momentum exchange method has been widely used in lattice Boltzmann simulations for particle-fluid interactions. Although proved accurate for still walls, it will result in inaccurate particle dynamics without corrections. In this work, we reveal the physical cause of this problem and find that the initial momentum of the net mass transfer through boundaries in the moving-boundary treatment is not counted in the conventional momentum exchange method. A corrected momentum exchange method is then proposed by taking into account the initial momentum of the net mass transfer at each time step. The method is easy to implement with negligible extra computation cost. Direct numerical simulations of a single elliptical particle sedimentation are carried out to evaluate the accuracy for our method as well as other lattice Boltzmann-based methods by comparisons with the results of the finite element method. A shear flow test shows that our method is Galilean invariant.

Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions.

The physical origin of severe low-frequency pressure fluctuation frequently observed in Francis hydraulic turbines under off-design conditions, which greatly damages the structural stability of turbines and even power stations, is analyzed based on the hydrodynamic stability theory and our Reynolds-averaged Navier-Stokes equation simulation (RANS) of the flow in the entire passage of a Francis turbine. We find that spontaneous unsteady vortex ropes, which induce severe pressure fluctuations, are formed due to the absolute instability of the swirling flow at the conical inlet of the turbine's draft tube.

The physical origin of severe low-frequency pressure fluctuations in giant francis turbines

The Ellipsoidal Statistical model (ES-model) and the Shakhov model (S- model) were constructed to correct the Prandtl number of the original BGK model through the modification of stress and heat flux. With the introduction of a new pa- rameter to combine the ES-model and S-model, a generalized kinetic model can be developed. This new model can give the correct Navier-Stokes equations in the con- tinuum flow regime. Through the adjustment of the new parameter, it provides abun- dant dynamic effect beyond the ES-model and S-model. Changing the free parameter, the physical performance of the new model has been tested numerically. The unified gas kinetic scheme (UGKS) is employed for the study of the new model. In transition flow regime, many physical problems, i.e., the shock structure and micro-flows, have been studied using the generalized model. With a careful choice of the free parameter, good results can be achieved for most test cases. Due to the property of the Boltz- mann collision integral, the new parameter in the generalized kinetic model cannot be fully determined. It depends on the specific problem. Generally speaking, the S- model predicts more accurate numerical solutions in most test cases presented in this paper than the ES-model, while ES-model performs better in the cases where the flow is mostly driven by temperature gradient, such as a channel flow with large boundary temperature variation at high Knudsen number. AMS subject classifications: 65M10, 78A48

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/94B69F87ABE4474413D5E5374C17B009/S2070073315000089a.pdf/div-class-title-a-comparison-and-unification-of-ellipsoidal-statistical-and-shakhov-bgk-models-div.pdf

Qingdong Cai

Papers

A unified gas-kinetic scheme for continuum and rarefied flows IV

A unified gas kinetic scheme with moving mesh and velocity space adaptation

Momentum-exchange method in lattice Boltzmann simulations of particle-fluid interactions.

The physical origin of severe low-frequency pressure fluctuations in giant francis turbines

A Comparison and Unification of Ellipsoidal Statistical and Shakhov BGK Models