This is the final project paper for HPC Fall 2012 course in New York University. In this paper, we describe an implemention of compressible inviscid fluid solvers on Graphics Processing Units using NVIDIA’s CUDA. Using the method of lines approach with the third order Runge-Kutta time integration scheme, piecewise linear reconstruction, and a Harten-Lax-van Leer Riemann solver, we achieve an ov...

A brief computational description of the Lin-Rood shallow water finite volume (SWfv) model is provided. Along side, salient features of the model are described. 4D-VAR data assimilation experiments using this model provided us avenues to study model error introduced by different high order advection schemes (such as van Leer and PPM) in the framework of 4D-variational data assimilation. This mo...

We study the magnetohydrodynamics (MHD) equations with anisotropic ion pressure and isotropic electron pressure under both the classical and semirelativistic approximations in order to develop a numerical model. The dispersion relation as well as the characteristic wave speeds are derived. In addition to the exact wave speed solutions, we also provide efficient approximate formulas for the semi...

In this paper, an accurate numerical model is presented for one-dimensional open-channel flows with varying topographies; the specifically applied to rectangular channels variable widths. A pressure term introduced in shallow water momentum equation construct a new conservation term, and resulting non-conservation included source characterize actual topography changes flow. Based on Harten Lax ...

—————————————————— Combining the results of tunneling, photoemission and thermodynamic studies, the pseudogap is unambiguously demonstrated to be caused by Van Hove nesting: a splitting of the density of states peak at (π, 0). The fact that the splitting remains symmetric about the Fermi level over an extended doping range indicates that the Van Hove singularity is pinned to the Fermi level. De...

This paper presents a class of novel high-order accurate discontinuous Galerkin (DG) schemes for the compressible Euler equations under gravitational fields. A notable feature these is that they are well-balanced general hydrostatic equilibrium state, and at same time, provably preserve positivity density pressure. In order to achieve positivity-preserving properties simultaneously, DG spatial ...

This paper presents a new two-phase density-based solver based on the finite difference method for simulating high-speed wet steam flows with non-equilibrium condensation. The employs Eulerian–Eulerian approach to model flow using fifth-order accurate weighted compact nonlinear scheme. phase change of involves droplet growth in condensation process internally consistent classical theory. To spe...

A multi-parameter family of optimal Euler preconditioners are explored. This uncovers the link between the various matrices derived by Van Leer et al. and Turkel, and also presents an attempt to derive more effective matrices. The preconditioning technique, which is based on a difference scheme rather than on partial differential equations, is extended from the Euler equations to the Navier-Sto...