An unsteady two-dimensional numerical investigation was performed on the viscous flow passing through a multi-blade cascade. A Cartesian finite-volume approach was employed and it was linked to Van-Leer's and Roe's flux splitting schemes to evaluate inviscid flux terms. To prevent the oscillatory behavior of numerical results and to increase the accuracy, Monotonic Upstream Scheme for Conservat...

In this note some stability results are derived for the Douglas splitting method. The relevance of the theoretical results is tested for an advection-reaction equation. 1. Presentation of the results Consider the initial value problem for a system of ODEs u′(t) = F (t, u(t)) (1.1) with 0 ≤ t ≤ T and given initial value u(0). We shall consider numerical schemes with step size τ yielding approxim...

In this paper, the exponential B-spline functions are used for the numerical solution of the advection-diffusion equation. Two numerical examples related to pure advection in a finitely long channel and the distribution of an initial Gaussian pulse are employed to illustrate the accuracy and the efficiency of the method. Obtained results are compared with some early studies.

Coupled multi-physics systems dominate computational models of advanced science and engineering applications. These systems give rise to challenges not typically faced by single-physics models: including interacting stiff and nonstiff processes, disparate time scales, increased nonlinearity and large data requirements. Historically, opposite approaches have been pursued by theoreticians and pra...

Effects of landfall location and approach angle on track deflection associated with a tropical cyclone (TC) passing over an idealized and Central Appalachian Mountain is investigated by a series of idealized numerical experiments. When the TC landfalls on the central portion of the mountain range, it is deflected to the south upstream, passes over the mountain anticyclonically, and then moves w...

A model for the simulation of complex three-dimensional free surface flows is presented. An incompressible liquid interacts with a compressible gas. The incompressible Navier-Stokes equations are solved only in the liquid domain while the dynamical effects in the gas are neglected. The compressibility effects of the gas are taken into account by computing its pressure. Surface tension effects a...

We present a WENO-TVD scheme for the simulation of atmospheric phenomena. The scheme considers a spatial discretization via a second-order TVD flux based upon a flux-centered limiter approach, which makes use of high-order accurate extrapolated values arising from a WENO reconstruction procedure. Time discretization is performed with a third order RK-TVD scheme, and splitting is used for the in...

This paper reviews mathematical models and numerical methods that have been extensively used to simulate the movement of contaminants through the subsurface. The major emphasis is placed on the numerical methods of advection-dominated transport problems and inverse problems. Several mathematical models that are commonly used in field problems are listed. A variety of numerical solutions for thr...

A forward-in-time splitting method for integrating the elastic equations is presented. A second-order Runge– Kutta time integrator (RK2) for the large-time-step integration is combined with the forward–backward scheme in a manner similar to the Klemp and Wilhelmson method. The new scheme produces fully second-order-accurate integrations for advection and gravity wave propagation. The RK2 scheme...

In this paper we study the error propagation of numerical schemes for the advection equation in the case where high precision is desired. The numerical methods considered are based on the fast Fourier transform, polynomial interpolation (semi-Lagrangian methods using a Lagrange or spline interpolation), and a discontinuous Galerkin semi-Lagrangian approach (which is conservative and has to stor...