Optimal and near-optimal advection-diffusion finite-difference schemes. Part 2: Unsteadiness and non-uniform grid
نویسنده
چکیده
∂tc+ λ c+ u ∂xc− κ ∂ xc = q + ∂xf + ∂ xg . At the grid points the extremely high order of approximation for the numerical solutions is such that if loss of accuracy is to be avoided then interpolation must use values extending beyond the local 3 by 2 computational module. Illustrative examples show that reasonable accuracy is possible with extremely long time steps on sparse non-uniform, moving grids.
منابع مشابه
Optimal and near-optimal advection-diffusion finite-difference schemes 4. Spatial non-uniformity
the non-uniformity can almost be removed with a local change of variables from c(s, t) to b(x, t). So, in numerical computations non-uniformity need not imply any reduction from optimal accuracy. A computational grid that was uniformly spaced with respect to s becomes non-uniform with respect to the intrinsic xcoordinate. Suitable non-uniform grid, optimal and near-optimal compact finitediffere...
متن کاملOptimal and near - optimal advection - diffusion finite - difference schemes . Part 1 : constant coefficient 1 - D
An implicit finite difference scheme is derived which achieves exact results for the area, centroid, variance, skewness and kurtosis (flatness) of solutions to the unforced advection-diffusion equation ∂ t c + λ c + u ∂ x c − κ ∂ 2 x c = 0. Sufficient conditions for computational stability are that the grid spacing ∆x and time step ∆t be small enough that |u| ∆x κ < 12 1/2 , |u| ∆t ∆x < 1 2 1/2...
متن کاملPositivity-preserving nonstandard finite difference Schemes for simulation of advection-diffusion reaction equations
Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...
متن کاملOptimal and near-optimal advection-diffusion finite-difference schemes VI. 2-D alternating directions
The 3 × 3 × 2 compact computational module involves three consecutive spatial points in each of the perpendicular spatial directions at two successive time levels. The schemes are tested for three variants of an exactly solvable test case, corresponding to the fractionation of an initial mixture of sinking, neutral, and rising particles released together in a vertically well-mixed turbulent ope...
متن کاملApproximation of stochastic advection diffusion equations with finite difference scheme
In this paper, a high-order and conditionally stable stochastic difference scheme is proposed for the numerical solution of $rm Ithat{o}$ stochastic advection diffusion equation with one dimensional white noise process. We applied a finite difference approximation of fourth-order for discretizing space spatial derivative of this equation. The main properties of deterministic difference schemes,...
متن کامل