We investigate the type I modes of instability within the compressible boundary-layer flow over a rotating cone, defined by general half angle ψ. The work extends previous studies into the compressible rotatingdisk flow (ψ = 90o) and incompressible rotating-cone flows. Generalised compressible von Kármán equations are established and solved numerically to give the laminar-flow profiles. We then...

The point-splitting regularization technique for composite operators is discussed in connection with anomaly calculation. We present a pedagogical and self-contained review of the topic with an emphasis on the technical details. We also develop simple algebraic tools to handle the path ordered exponential insertions used within the covariant and non-covariant version of the point-splitting meth...

1. R. Hargreaves, A pressure-integral as kinetic potential, Phil. Mag. 436-444 (1908). 2. H. Bateman, Notes on a differential equation which occurs in the two-dimensional motion of a compressible fluid and the associated variational problems, Proc. Roy. Soo. London (A) 125, 598-618 (1929). 3. Chi-Teh Wang, Variational method in the theory of compressible fluid, J. of Aero. Sciences 15, 675-685 ...

We generalize Horrocks’ criterion for the splitting of vector bundles on projective space. We establish an analogous splitting criterion for vector bundles on arbitrary smooth complex projective varieties of dimension ≥ 4, which asserts that a vector bundle E on X splits iff its restriction E|Y to an ample smooth codimension 1 subvariety Y ⊂ X splits.

Here we extend the flux vector splitting approach recently proposed in (E F Toro and M E Vázquez-Cendón. Flux splitting schemes for the Euler equations. Computers and Fluids. Vol. 70, Pages 1-12, 2012). The scheme was originally presented for the 1D Euler equations for ideal gases and its extension presented in this paper is threefold: (i) we solve the three-dimensional Euler equations on gener...

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...

Our goal is to present a simple interface-capturing approach for barotropic two-fluid flow problems in more than one space dimension. We use the compressible Euler equations in isentropic form as a model system with the thermodynamic property of each fluid component characterized by the Tait equation of state. The algorithm uses a non-isentropic form of the Tait equation of state as a basis to ...

We apply the gas-kinetic scheme (GKS) for the direct numerical simulations (DNSs) of compressible decaying homogeneous isotropic turbulence (DHIT). We intend to study the accuracy, stability, and efficiency of the gas-kinetic scheme for DNS of compressible homogeneous turbulence depending on both flow conditions and numerics. In particular, we study the GKS with multidimensional, quasi-one-dime...

We establish forward and backward relations between entropy satisfying BGK models such as those introduced previously by the author and the rst order ux vector splitting numerical methods for systems of conservation laws. Classically, to a kinetic BGK model that is compatible with some family of entropies we can associate an entropy ux vector splitting. We prove that the converse is true: any e...