Central Schemes for Porous Media Flows

We are concerned with central differencing schemes for solving scalar hyperbolic conservation laws arising in the simulation of multiphase flows in heterogeneous porous media. We compare the Kurganov-Tadmor, 2000 semi-discrete central scheme with the Nessyahu-Tadmor, 1990 central scheme. The KT scheme uses more precise information about the local speeds of propagation together with integration over nonuniform control volumes, which contain the Riemann fans. These methods can accurately resolve sharp fronts in the fluid saturations without introducing spurious oscillations or excessive numerical diffusion. We first discuss the coupling of these methods with velocity fields approximated by mixed finite elements. Then, numerical simulations are presented for two-phase, two-dimensional flow problems in multi-scale heterogeneous petroleum reservoirs. We find the KT scheme to be considerably less diffusive, particularly in the presence of high permeability flow channels, which lead to strong restrictions on the time step selection; however, the KT scheme may produce incorrect boundary behavior

Mesonic states in the generalised Nambu-Jona-Lasinio theories

For any Nambu-Jona-Lasinio model of QCD with arbitrary nonlocal, instantaneous, quark current-current confining kernels, we use a generalised Bogoliubov technique to go beyond BCS level (in the large-Nc limit) so as to explicitly build quark-antiquark compound operators for creating/annihilating mesons. In the Hamiltonian approach, the mesonic bound-state equations appear (from the generalised Bogoliubov transformation) as mass-gap-like equations which, in turn, ensure the absence, in the Hamiltonian, of mesonic Bogoliubov anomalous terms. We go further to demonstrate the one-to-one correspondence between Hamiltonian and Bethe-Salpeter approaches to non-local NJL-type models for QCD and give the corresponding "dictionary" necessary to "translate" the amplitudes built using the graphical Feynman rules to the terms of the Hamiltonian, and vice versa. We comment on the problem of multiple vacua existence in such type of models and argue that mesonic states in the theory should be prescribed to have an extra index - the index of the replica in which they are created. Then the completely diagonalised Hamiltonian should contain a sum over this new index. The method is proved to be general and valid for any instantaneous quark kernel.Comment: LaTeX2e, uses aipproc class, Talk given at the conference "Quark Confinement and the Hadron Spectrum VI", 21-25 September 2004, Sardinia, Italy, to appear in Proceeding

Quantum field theory approach to the vacuum replica in QCD

Quantum field theory is used to describe the contribution of possible new QCD vacuum replica to hadronic processes. This sigma-like new state has been recently shown to be likely to appear for any realistic four-quark interaction kernel as a consequence of chiral symmetry. The local operator creating the replica vacuum state is constructed explicitly. Applications to physical processes are outlined.Comment: LaTeX2e, 2 EPS figures, uses ws-procs9x6 (included) and epsfig classes, Talk given at the conference "Quark Confinement and the Hadron Spectrum V", 10-14 September 2002, Gargnano, Italy, to appear in Proceeding

DNS of Laminar to Turbulent Transition on NACA 0012 Airfoil with Sand Grain Roughness

The Lattice-Boltzmann-based solver PowerFLOW is used to perform direct numerical simulations of the transitional flow over an airfoil at Reynolds number equal to 0.657 million. The leading edge of the airfoil is covered with sand particles, represented by polyhedra, to mimic the grit used in experiments. The sensitivity of the laminar to turbulent transition to the size of these particles, grid resolution, spanwise length is evaluated and rectangular trips are also tested