High order moment closure for Vlasov-Maxwell equations

The extended magnetohydrodynamic models are derived based on the moment closure of the Vlasov-Maxwell （VM） equations. We adopt the Grad type moment expansion which was firstly proposed for the Boltzmann equation. A new regularization method for the Grad＇s moment system was recently proposed to achieve the globally hyperbolicity so that the local well-posedness of the moment system is attained. For the VM equations, the moment expansion of the convection term is exactly the same as that in the Boltzmann equation, thus the new developed regularization applies. The moment expansion of the electromagnetic force term in the VM equations turns out to be a linear source term, which can preserve the conservative properties of the distribution function in the VM equations perfectly.

AN ADAPTIVE FAST INTERFACE TRACKING METHOD

An adaptive numerical scheme is developed for the propagation of an interface in a velocity field based on the fast interface tracking method proposed in [2]. A multiresolution stategy to represent the interface instead of point values, allows local grid refinement while controlling the approximation error on the interface. For time integration, we use an explicit Runge-Kutta scheme of second-order with a multiseale time step, which takes longer time steps for finer spatial scales. The implementation of the algorithm uses a dynamic tree data structure to represent data in the computer memory. We briefly review first the main algorithm, describe the essential data structures, highlight the adaptive scheme, and illustrate the computational efficiency by some numerical examples.

A General Moving Mesh Framework in 3D and its Application for Simulating the Mixture of Multi-Phase Flows

In this paper, we present an adaptive moving mesh algorithm for meshesof unstructured polyhedra in three space dimensions. The algorithm automaticallyadjusts the size of the elements with time and position in the physical domain to resolvethe relevant scales in multiscale physical systems while minimizing computationalcosts. The algorithm is a generalization of the moving mesh methods basedon harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To make 3D moving mesh simulations possible,the key is to develop an efficient mesh redistribution procedure so that this part willcost as little as possible comparing with the solution evolution part. Since the meshredistribution procedure normally requires to solve large size matrix equations, wewill describe a procedure to decouple the matrix equation to a much simpler blocktridiagonaltype which can be efficiently solved by a particularly designed multi-gridmethod. To demonstrate the performance of the proposed 3D moving mesh strategy,the algorithm is implemented in finite element simulations of fluid-fluid interface interactionsin multiphase flows. To demonstrate the main ideas, we consider the formationof drops by using an energetic variational phase field model which describesthe motion of mixtures of two incompressible fluids. Numerical results on two- andthree-dimensional simulations will be presented.

Moving Mesh Kinetic Simulation for Sheared Rodlike Polymers with High Potential Intensities

The Doi-Hess equation that describes the evolution of an orientational dis-tribution function is capable of predicting several rheological features of nematic poly-mers.Since the orientational distribution function becomes sharply peaked as poten-tial intensity increases,powerful numerical methods become necessary in the relevant numerical simulations.In this paper,a numerical scheme based on the moving grid techniques will be designed to solve the orientational distribution functions with high potential intensities.Numerical experiments are carried out to demonstrate the effec-tiveness and robustness of the proposed scheme.