A Variational Multiscale Method for Particle Dispersion Modeling in the Atmosphere

A LES model is proposed to predict the dispersion of particles in the atmosphere in the context of Chemical,Biological,Radiological and Nuclear(CBRN)applications.The code relies on the Finite Element Method(FEM)for both the fluid and the dispersed solid phases.Starting from the Navier-Stokes equations and a general description of the FEM strategy,the Streamline Upwind Petrov-Galerkin(SUPG)method is formulated putting some emphasis on the related assembly matrix and stabilization coefficients.Then,the Variational Multiscale Method(VMS)is presented together with a detailed illustration of its algorithm and hierarchy of computational steps.It is demonstrated that the VMS can be considered as a more general version of the SUPG method.The final part of the work is used to assess the reliability of the implemented predictor/multicorrector solution strategy.

A Finite Element Variational Multiscale Method for Stationary Incompressible Magnetohydrodynamics Equations

In this paper,we propose a variational multiscale method(VMM)for the stationary incompressible magnetohydrodynamics equations.This method is defined by large-scale spaces for the velocity field and the magnetic field,which aims to solve flows at high Reynolds numbers.We provide a new VMM formulation and prove its stability and convergence.Finally,some numerical experiments are presented to indicate the optimal convergence of our method.

A Dimension-Splitting Variational Multiscale Element-Free Galerkin Method for Three-Dimensional Singularly Perturbed Convection-Diffusion Problems

By introducing the dimensional splitting(DS)method into the multiscale interpolating element-free Galerkin(VMIEFG)method,a dimension-splitting multiscale interpolating element-free Galerkin(DS-VMIEFG)method is proposed for three-dimensional(3D)singular perturbed convection-diffusion(SPCD)problems.In the DSVMIEFG method,the 3D problem is decomposed into a series of 2D problems by the DS method,and the discrete equations on the 2D splitting surface are obtained by the VMIEFG method.The improved interpolation-type moving least squares(IIMLS)method is used to construct shape functions in the weak form and to combine 2D discrete equations into a global system of discrete equations for the three-dimensional SPCD problems.The solved numerical example verifies the effectiveness of the method in this paper for the 3D SPCD problems.The numerical solution will gradually converge to the analytical solution with the increase in the number of nodes.For extremely small singular diffusion coefficients,the numerical solution will avoid numerical oscillation and has high computational stability.

New nonconforming finite element method for solving transient Naiver-Stokes equations

For transient Naiver-Stokes problems, a stabilized nonconforming finite element method is presented, focusing on two pairs inf-sup unstable finite element spaces, i.e., pNC/pNC triangular and pNQ/pNQ quadrilateral finite element spaces. The semi- and full-discrete schemes of the stabilized method are studied based on the pressure projection and a variational multi-scale method. It has some attractive features： avoiding higher-order derivatives and edge-based data structures, adding a discrete velocity term only on the fine scale, being effective for high Reynolds number fluid flows, and avoiding increased computation cost. For the full-discrete scheme, it has second-order estimations of time and is unconditionally stable. The presented numerical results agree well with the theoretical results.

Numerical investigation on fluid forces of piggyback circular cylinders in tandem arrangement at low Reynolds numbers

Numerical simulations of flows past the piggyback circular cylinders in tandem arrangement are performed by solving the variational multiscale formulation of the incompressible Navier-Stokes equations using in-house finite element method(FEM)codes.The effects of the gap-spacing-to-diameter(G/D)and the two diameter ratio(d/D)on the flow characteristics and the reductions of the root-mean-square(RMS)drag and lift coefficients are considered for Reynolds numbers(Res)are 100 and 200.The validation shows the fluid force coefficients obtained by the in-house FEM codes are in good agreement with the results in the existing literatures.The obtained results show that,with a proper placement of the smaller cylinder(d/D=0.2)behind the larger cylinder,the RMS drag and lift coefficients largely decrease compared to those of the single circular cylinder.When d/D=0.2,the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at G/D=1.2 as Re=100 and at G/D=1.0 as Re=200.It is observed that the proper placement of the smaller cylinder causes the surrounding vorticity to take opposite sign with the vorticity in the outer region so as to suppress and postpone the vortex shedding in the wake,and that the different positions of the vortex shedding at two Res cause that the largest reductions of the RMS lift coefficient of the larger cylinder and the RMS total lift coefficient appear at different G/D as Re is different.When d/D varies,the variation of the RMS total lift coefficient behaves differently at two Res.It decreases with J/D increasing at Re=100,while it no longer monotonously varies with J/D,but reaches a minimum in the considered range of d/D at Re=200.Moreover,the larger d/D results in stronger suppression and postponement of the vortex shedding in the wake.