A Conservative Discontinuous Galerkin Scheme With O(N-2) Operations In Computing Boltzmann Collision Weight Matrix

In the present work, we propose a deterministic numerical solver for the homogeneous Boltzmann equation based on Discontinuous Galerkin (DG) methods. The weak form of the collision operator is approximated by a quadratic form in linear algebra setting. We employ the property of >shifting symmetry> in the weight matrix to reduce the computing complexity from theoretical O(N-3) down to O(N-2), with N the total number of freedom for d-dimensional velocity space. In addition, the sparsity is also explored to further reduce the storage complexity. To apply lower order polynomials and resolve loss of conserved quantities, we invoke the conservation routine at every time step to enforce the conservation of desired moments (mass, momentum and/or energy), with only linear complexity. Due to the locality of the DG schemes, the whole computing process is well parallelized using hybrid OpetiMP and MPI. The current work only considers integrable angular cross-sections under elastic and/or inelastic interaction laws. Numerical results on 2-D and 3-D problems are shown.Mathematic

Toward an anisotropic atom-atom model for the crystalline phases of the molecular S8 compound

We analize two anisotropic atom-atom models used to describe the crystalline alpha,beta and gamma phases of S8 crystals, the most stable compound of elemental sulfur in solid phases, at ambient pressure and T<=400 K. The calculations are performed via a series of classical molecular dynamics (MD) simulations, with flexible molecular models and using a constant pressure-constant temperature algorithm for the numerical simulations. All intramolecular modes that mix with lattice modes, and are therefore relevant on the onset of structural phase transitions, are taken into account. Comparisons with experimental data and previous results obtained with an isotropic atom-atom molecular model are also performed.Comment: Major changes, new simulations and figures added, revtex4, to appear in J. Chem. Phy

Test of a simple and flexible molecule model for alpha-, beta- and gamma-S8 crystals

S8 is the most stable compound of elemental sulfur in solid and liquid phases, at ambient pressure and below 400K. Three crystalline phases of S8 have been clearly identified in this range of thermodynamic parameters, although no calculation of its phase diagram has been performed yet. alpha- and gamma-S8 are orientationally ordered crystals while beta-S8 is measured as orientationally disordered. In this paper we analyze the phase diagram of S8 crystals, as given by a simple and flexible molecule model, via a series of molecular dynamics (MD) simulations. The calculations are performed in the constant pressure- constant temperature ensemble, using an algorithm that is able to reproduce structural phase transitions.Comment: RevTex,7 pages, 5 figures,to appear in J. Chem. Phy

A discontinuous Galerkin method for the Vlasov-Poisson system

A discontinuous Galerkin method for approximating the Vlasov-Poisson system of equations describing the time evolution of a collisionless plasma is proposed. The method is mass conservative and, in the case that piecewise constant functions are used as a basis, the method preserves the positivity of the electron distribution function and weakly enforces continuity of the electric field through mesh interfaces and boundary conditions. The performance of the method is investigated by computing several examples and error estimates associated system's approximation are stated. In particular, computed results are benchmarked against established theoretical results for linear advection and the phenomenon of linear Landau damping for both the Maxwell and Lorentz distributions. Moreover, two nonlinear problems are considered: nonlinear Landau damping and a version of the two-stream instability are computed. For the latter, fine scale details of the resulting long-time BGK-like state are presented. Conservation laws are examined and various comparisons to theory are made. The results obtained demonstrate that the discontinuous Galerkin method is a viable option for integrating the Vlasov-Poisson system.Comment: To appear in Journal for Computational Physics, 2011. 63 pages, 86 figure