The gas-kinetic theory based flux splitting method has been successfully proposed for solving one- and two-dimensional ideal magnetohydrodynamics by Xu et al.[J. Comput. Phys., 1999; 2000], respectively. This paper extends the kinetic method to solve three-dimensional ideal magnetohydrodynamics equations, where an adaptive parameter η is used to control the numerical dissipation in the flux splitting method.Several numerical examples are given to demonstrate that the proposed method can achieve high numerical accuracy and resolve strong discontinuous waves in three dimensional ideal MHD problems.
As a continuation of a recent linear analysis by Mao et al.(Acta Mech Sin,2010,26:355),in this paper we propose a general theoretical formulation for the compressing process in complex Newtonian fluid flows,which covers gas dynamics,aeroacoustics,nonlinear thermoviscous acoustics,viscous shock layer,etc.,as its special branches.The principle on which our formulation is based is the maximally natural and dynamic Helmholtz decomposition of the Navier-Stokes equation,along with the kinematic Helmholtz decomposition of the velocity field.The central results are the new dilatation equation and velocity-potential equation,which are the counterparts of vorticity transport equation and vector stream-function equation for the shearing process,respectively.Various couplings of the compressing process with shearing and thermal processes,including its physical sources,are carefully identified.While the possible applications and influences of the new formulation are yet to be explored,our preliminary discussion on the pros and cons of previous formulations pertain to acoustic analogy and that on the process splitting and coupling in highly compressible turbulence indicates that at least the formulation can serve as a new frame of reference by which one may gain some additional insight and thereby develop new approaches to the multi-process complex flow problems.
By Green's function method we show that the water hammer (WH) can be analytically predicted for both laminar and turbulent flows (for the latter,with an eddy viscosity depending solely on the space coordinates),and thus its hazardous effect can be rationally controlled and minimized.To this end,we generalize a laminar water hammer equation of Wang et al.(J.Hydrodynamics,B2,51,1995) to include arbitrary initial condition and variable viscosity,and obtain its solution by Green's function method.The predicted characteristic WH behaviors by the solutions are in excellent agreement with both direct numerical simulation of the original governing equations and,by adjusting the eddy viscosity coefficient,experimentally measured turbulent flow data.Optimal WH control principle is thereby constructed and demonstrated.
With discretized particle velocity space,a multi-scale unified gas-kinetic scheme for entire Knudsen number flows has been constructed based on the kinetic model in one-dimensional case[J.Comput.Phys.,vol.229(2010),pp.7747-7764].For the kinetic equation,to extend a one-dimensional scheme to multidimensional flow is not so straightforward.The major factor is that addition of one dimension in physical space causes the distribution function to become two-dimensional,rather than axially symmetric,in velocity space.In this paper,a unified gas-kinetic scheme based on the Shakhov model in two-dimensional space will be presented.Instead of particle-based modeling for the rarefied flow,such as the direct simulation Monte Carlo(DSMC)method,the philosophical principal underlying the current study is a partial-differential-equation(PDE)-based modeling.Since the valid scale of the kinetic equation and the scale of mesh size and time step may be significantly different,the gas evolution in a discretized space is modeled with the help of kinetic equation,instead of directly solving the partial differential equation.Due to the use of both hydrodynamic and kinetic scales flow physics in a gas evolution model at the cell interface,the unified scheme can basically present accurate solution in all flow regimes from the free molecule to the Navier-Stokes solutions.In comparison with the DSMC and Navier-Stokes flow solvers,the current method is much more efficient than DSMC in low speed transition and continuum flow regimes,and it has better capability than NS solver in capturing of non-equilibrium flow physics in the transition and rarefied flow regimes.As a result,the current method can be useful in the flow simulation where both continuum and rarefied flow physics needs to be resolved in a single computation.This paper will extensively evaluate the performance of the unified scheme fromfreemolecule to continuum NS solutions,and fromlow speedmicro-flow to high speed non-equilibrium aerodynamics.The test cases clearly demonstrate tha
With the development of computational power and numerical algorithms,computational fluid dynamics(CFD) has become an important strategy for the design of aircraft,which significantly reduces the reliance on wind-tunnel and flight tests.In this paper,we conducted a numerical investigation on the flow past a full commercial aircraft at Mach number 0.2 and 14 degrees angle of attack by means of Reynolds-averaged Navier-Stokes(RANS),detached-eddy simulation(DES) and our newly developed constrained large-eddy simulation(CLES).The objective of this paper is to study the capability of these models in simulating turbulent flows.To our knowledge,this is the first large-eddy simulation method for full commercial aircraft simulation.The results show that the CLES can predict the mean statistical quantities well,qualitatively consistent with traditional methods,and can capture more small-scale structures near the surface of the aircraft with massive separations.Our study demonstrates that CLES is a promising alternative for simulating real engineering turbulent flows.
Compressible flow past a circular cylinder at an inflow Reynolds number of 2×105 is numerically investigated by using a constrained large-eddy simulation(CLES)technique.Numerical simulation with adiabatic wall boundary condition and at a free-stream Mach number of 0.75 is conducted to validate and verify the performance of the present CLES method in predicting separated flows.Some typical and characteristic physical quantities,such as the drag coefficient,the root-mean-square lift fluctuations,the Strouhal number,the pressure and skin friction distributions around the cylinder,etc.are calculated and compared with previously reported experimental data,finer-grid large-eddy simulation(LES)data and those obtained in the present LES and detached-eddy simulation(DES)on coarse grids.It turns out that CLES is superior to DES in predicting such separated flow and that CLES can mimic the intricate shock wave dynamics quite well.Then,the effects of Mach number on the flow patterns and parameters such as the pressure,skin friction and drag coefficients,and the cylinder surface temperature are studied,with Mach number varying from 0.1 to 0.95.Nonmonotonic behaviors of the pressure and skin friction distributions are observed with increasing Mach number and the minimum mean separation angle occurs at a subcritical Mach number of between 0.3 and 0.5.Additionally,the wall temperature effects on the thermodynamic and aerodynamic quantities are explored in a series of simulations using isothermal wall boundary conditions at three different wall temperatures.It is found that the flow separates earlier from the cylinder surface with a longer recirculation length in the wake and a higher pressure coefficient at the rear stagnation point for higher wall temperature.Moreover,the influences of different thermal wall boundary conditions on the flow field are gradually magnified from the front stagnation point to the rear stagnation point.It is inferred that the CLES approach in its current version is a useful and effective tool for sim
