A three-dimensional, three-phase numerical model is presented for simulating the movement of non-aqueous-phase liquids (NAPL's) through porous and fractured media. The model is designed for practical applica:ion to a wide variety of contamination and remediation scenarios involving light or dense NAPL's in heterogeneous subsurface systems. The model formulation is first derived for three-phase ...

This paper presents the formulation of a dual time stepping procedure to solve the equations of fully implicit Runge–Kutta schemes. In particular themethod is applied toGauss and Radau 2A schemes with either two or three stages. The schemes are tested for unsteady flows over a pitching airfoil modeled by both the Euler and the unsteady Reynolds averaged Navier Stokes equations. It is concluded ...

A family of implicit-explicit second order time-stepping methods is analyzed for a system of ODEs motivated by ones arising from spatial discretizations of evolutionary partial differential equations. The methods we consider are implicit in local and stabilizing terms in the underlying PDE and explicit in nonlocal and unstabilizing terms. Unconditional stability and convergence of the numerical...

For the simulation of waves in a bounded domain, the absorbing boundary condition (ABC) must be set appropriately to suppress the wave reflection on the boundary. This article introduces a new traveltime-based ABC which can significantly reduce the boundary reflection. Also the article considers a new fourth-order implicit time-stepping scheme, which incorporates a locally one-dimensional proce...

Explicit numerical methods for the solution of a system of stiff differential equations suffer from a time step size that approaches zero in order to satisfy stability conditions. Implicit schemes allow a larger time-step, but require more computations. When the differential equations are dominated by a skew-symmetric component, the problem is not stiffness in the sense that the size of the eig...

This paper presents a new class of high order linear ImEx multistep schemes with large regions of unconditional stability. Unconditional stability is a desirable property of a time stepping scheme, as it allows the choice of time step solely based on accuracy considerations. Of particular interest are problems for which both the implicit and explicit parts of the ImEx splitting are stiff. Such ...

Three new fully implicit methods which are based on the (5,5) Crank–Nicolson method, the (5,5) N-H (Noye–Hayman) implicit method and the (9,9) N-H implicit method are developed for solving the heat equation in two dimensional space with non-local boundary conditions. The latter is fourth-order while the others are second-order. While the implicit methods developed here, like the scheme based on...