Finite difference method

Abstract: To study radio wave propagation in tunnels, we present a vectorial parabolic equation (PE) taking into account the cross-section shape, wall impedances, slowly varying curvature, and torsion of the tunnel axis. For rectangular cross section, two polarizations are decoupled and two families of adiabatic modes can be found explicitly, giving a generalization of the known results for a uniform tunnel. In the general case, a boundary value problem arises to be solved by using finite-difference/finite-element (FD/FE) techniques. Numerical examples demonstrate the computational efficiency of the proposed method.

Abstract: The forward problem in electrophysiology?the computation of the potential distribution due to a known electrical source in a known volume conductor?is discussed. Three methods of solution are considered: 1) the finite difference method 2) a discretized integral equation method 3) the analytic method.

Abstract: The direct numerical simulation (DNS) of the Taylor–Couette flow in the fully turbulent regime is described. The numerical method extends the work by Quadrio and Luchini [M. Quadrio, P. Luchini, Eur. J. Mech. B/Fluids 21 (2002) 413–427], and is based on a parallel computer code which uses mixed spatial discretization (spectral schemes in the homogeneous directions, and fourth-order, compact explicit finite-difference schemes in the radial direction). A DNS is carried out to simulate for the first time the turbulent Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information, with a view to compare it to planar, pressure-driven turbulent flow at the same value of the Reynolds number. The main source for differences in flow statistics between plane and curved-wall flows is attributed to the presence of large-scale rotating structures generated by curvature effects.