We present a new splitting method for time-dependent convention-dominated diffusion problems. The original convention diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a convection problem and a diffusion problem are solved successively. A few important features of the scheme lie in the facts that the convection subproblem is sol...

Generally, two approaches have been used to study the nonlinear wave-structure interaction in the context of offshore engineering in recent years. One is based on the Stokes perturbation procedure in the frequency domain and has been applied to weak-nonlinear problems. The other is based on a full nonlinear solution to the resulting wave field by a time-stepping procedure with boundary conditio...

An optimized explicit low-storage fourth-order Runge–Kutta algorithm is proposed in the present work for time integration. Dispersion and dissipation of the scheme are minimized in the Fourier space over a large range of frequencies for linear operators while enforcing a wide stability range. The scheme remains of order four with nonlinear operators thanks to the low-storage algorithm. Linear a...

We investigate a projective integration scheme for a kinetic equation in the limit of vanishing mean free path, in which the kinetic description approaches a diffusion phenomenon. The scheme first takes a few small steps with a simple, explicit method, such as a spatial centered flux/forward Euler time integration, and subsequently projects the results forward in time over a large time step on ...

In the field of strong-stability-preserving time discretizations, a number of researchers have considered using both upwind and downwind approximations for the same derivative, in order to guarantee that some strong stability condition will be preserved. The cost of computing both the upwind and downwind operator has always been assumed to be double that of computing only one of the two. Howeve...

The efficiency of high order accurate schemes for the solution of unsteady hyperbolic conservation laws is adversely affected by time-step restrictions that arise from monotonicity requirements. When applied to the solution of problems involving discontinuities, these restrictions render conventional high order implicit time integration schemes impractical. In the present study, a new single st...

The application of fourth-order finite difference discretisations of the second derivative of concentration with respect to distance from the electrode, in electrochemical digital simulations, is examined further. In the bulk of the diffusion space, a central 5-point scheme is used, and 6-point asymmetric schemes are used at the edges. In this paper, four Runge-Kutta schemes have been used for ...

Matrix Riccati Differential Equations (MRDEs) are initial value problems of the form: X 0 1⁄4 A21 XA11 þ A22X XA12X; Xð0Þ 1⁄4 X0: These equations arise frequently throughout applied mathematics, science, and engineering. It can happen that even when the Aij are smooth functions of t or constant, the solution X may have a singularity or even infinitely many singularities. This paper shows severa...

The aim of this paper is to study the convergence properties of a time marching algorithm solving advection-diffusion problems on two domains using incompatible discretizations. The basic algorithm is first described, and theoretical and numerical results that illustrate its convergence properties are then presented.