THEORY AND CONSERVATION THEOREM OF VORTICITY FLUX IN TRANSPORT

According to the theory of the transport and vorticity dynamics,the paper establishes the theory of vorticity flux and the conservation theorem between the vorticity flux and vortex strength in a plane flow.The theory of vorticity flux is a basic one in research on turbulence.

Validation of a novel mixing-plane method for multistage turbomachinery steady flow analysis

The steady calculation based on the mixing-plane method is still the most widely-used three-dimensional flow analysis tool for multistage turbomachines. For modern turbomachines,the trend of design is to reach higher aerodynamic loading but with still further compact size. In such a case, the traditional mixing-plane method has to be revised to give a more physically meaningful prediction. In this paper, a novel mixing-plane method was proposed, and three representative test cases including a transonic compressor, a highly-loaded centrifugal compressor and a highpressure axial turbine were performed for validation purpose. This novel mixing-plane method can satisfy the flux conservation perfectly. Reverse flow across the mixing-plane interface can be resolved naturally, thus making this method numerically robust. Artificial reflection at the mixing-plane interface is almost eliminated, and then its detrimental impact on the flow field is minimized. Generally, this mixing-plane method is suitable to simulate steady flows in highly-loaded multistage turbomachines.

The Locally Conservative Galerkin (LCG) Method — a Discontinuous Methodology Applied to a Continuous Framework

This paper presents a comprehensive overview of the element-wise locally conservative Galerkin(LCG)method.The LCG method was developed to find a method that had the advantages of the discontinuous Galerkin methods,without the large computational and memory requirements.The initial application of the method is discussed,to the simple scalar transient convection-diffusion equation,along with its extension to the Navier-Stokes equations utilising the Characteristic Based Split(CBS)scheme.The element-by-element solution approach removes the standard finite element assembly necessity,with an face flux providing continuity between these elemental subdomains.This face flux provides explicit local conservation and can be determined via a simple small post-processing calculation.The LCG method obtains a unique solution from the elemental contributions through the use of simple averaging.It is shown within this paper that the LCG method provides equivalent solutions to the continuous(global)Galerkin method for both steady state and transient solutions.Several numerical examples are provided to demonstrate the abilities of the LCG method.

Vlasov-Fokker-Planck Simulations for High-Power Laser-Plasma Interactions

A review is presented on our recent Vlasov-Fokker-Planck(VFP)simulation code development and applications for high-power laser-plasma interactions.Numerical schemes are described for solving the kinetic VFP equation with both electronelectron and electron-ion collisions in one-spatial and two-velocity(1D2V)coordinates.They are based on the positive and flux conservation method and the finite volume method,and these twomethods can insure the particle number conservation.Our simulation code can deal with problems in high-power laser/beam-plasma interactions,where highly non-Maxwellian electron distribution functions usually develop and the widely-used perturbation theories with the weak anisotropy assumption of the electron distribution function are no longer in point.We present some new results on three typical problems:firstly the plasma current generation in strong direct current electric fields beyond Spitzer-H¨arm’s transport theory,secondly the inverse bremsstrahlung absorption at high laser intensity beyond Langdon’s theory,and thirdly the heat transport with steep temperature and/or density gradients in laser-produced plasma.Finally,numerical parameters,performance,the particle number conservation,and the energy conservation in these simulations are provided.

AMaximum-Principle-Preserving Finite Volume Scheme for Diffusion Problems on Distorted Meshes

In this paper,we propose an approach for constructing conservative and maximum-principle-preserving finite volume schemes by using the method of undetermined coefficients,which depend nonlinearly on the linear non-conservative onesided fluxes.In order to facilitate the derivation of expressions of these undetermined coefficients,we explicitly provide a simple constriction condition with a scaling parameter.Such constriction conditions can ensure the final schemes are exact for linear solution problems and may induce various schemes by choosing different values for the parameter.In particular,when this parameter is taken to be 0,the nonlinear terms in our scheme degenerate to a harmonic average combination of the discrete linear fluxes,which has often been used in a variety of maximum-principle-preserving finite volume schemes.Thus our method of determining the coefficients of the nonlinear terms is more general.In addition,we prove the convergence of the proposed schemes by using a compactness technique.Numerical results demonstrate that our schemes can preserve the conservation property,satisfy the discrete maximum principle,possess a second-order accuracy,be exact for linear solution problems,and be available for anisotropic problems on distorted meshes.

A One-Dimensional Second-Order Cell-Centered Lagrangian Scheme Satisfying the Entropy Condition

The numerical solutions of gas dynamics equations have to be consistent with the second law of thermodynamics,which is termed entropy condition.However,most cell-centered Lagrangian(CL)schemes do not satisfy the entropy condition.Until 2020,for one-dimensional gas dynamics equations,the first-order CL scheme with the hybridized flux developed by combining the acoustic approximate(AA)flux and the entropy conservative(EC)flux developed by Maire et al.was used.This hybridized CL scheme satisfies the entropy condition;however,it is under-entropic in the part zones of rarefaction waves.Moreover,the EC flux may result in nonphysical numerical oscillations in simulating strong rarefaction waves.Another disadvantage of this scheme is that it is of only first-order accuracy.In this paper,we firstly construct a modified entropy conservative(MEC)flux which can damp effectively numerical oscillations in simulating strong rarefaction waves.Then we design a new hybridized CL scheme satisfying the entropy condition for one-dimensional complex flows.This new hybridized CL scheme is a combination of the AA flux and the MEC flux.In order to prevent the specific entropy of the hybridized CL scheme from being under-entropic,we propose using the third-order TVD-type Runge-Kutta time discretization method.Based on the new hybridized flux,we develop the second-order CL scheme that satisfies the entropy condition.Finally,the characteristics of our new CL scheme using the improved hybridized flux are demonstrated through several numerical examples.