A class of upwind flux splitting methods in the Euler equations of compressible flow is considered in this paper. Using the property that Euler flux F (U) is a homogeneous function of degree one in U , we reformulate the splitting fluxes with F+ = A+U , F− = A−U , and the corresponding matrices are either symmetric or symmetrizable and keep only non-negative and non-positive eigenvalues. That l...

A class of high-order kinetic flux vector splitting schemes are presented for solving ideal quantum gas dynamics based on quantum statistical mechanics. The collisionless quantum Boltzmann equation approach is adopted and both Bose– Einstein and Fermi–Dirac gases are considered. The formulas for the split flux vectors are derived based on the general three-dimensional distribution function in v...

BACKGROUND The extant roe deer (Capreolus Gray, 1821) includes two species: the European roe deer (C. capreolus) and the Siberian roe deer (C. pygargus) that are distinguished by morphological and karyotypical differences. The Siberian roe deer occupies a vast area of Asia and is considerably less studied than the European roe deer. Modern systematics of the Siberian roe deer remain controversi...

One reason which makes Roe’s Riemann solver attractive is its low computational cost. But the main drawback with Roe’s approximate Riemann solver is that non-physical expansion shocks can occur in the sonic points, it has been early remarked that for this particular situation. The Roe flux does not satisfy the entropy condition. In this paper an elegant response has been proposed by combining H...

A low diffusive flux difference splitting based kinetic scheme is developed on a discrete velocity Boltzmann equation, with novel three model. While two velocities are used for upwinding, the third utilized to introduce appropriate additional numerical diffusion only in expansion regions, identified using relative entropy (Kullback–Liebler divergence) at cell-interface, along estimation of phys...

The application of the Gaussian moment closure to micron-scale flows is considered. The mathematical formulation of the closure is reviewed as well as an extension to allow for diatomic gases and treatment for solid wall boundaries. A parallel upwind finite-volume scheme with adaptive mesh refinement (AMR) using Roe and HLLE-type flux functions is described for solving the hyperbolic system of ...

The flux-corrected transport (FCT) methodology is generalized to implicit finite element schemes and applied to the Euler equations of gas dynamics. The underlying low-order scheme is constructed by applying scalar artificial viscosity proportional to the spectral radius of the cumulative Roe matrix. All conservative matrix manipulations are performed edge-by-edge which leads to an efficient al...