A Two-Weight Scheme for a Time-Dependent Advection-Diffusion Problem

Chadha, Naresh M.; Madden, Niall

doi:10.1007/978-3-642-19665-2_11

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2021

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Cited by 2 publications

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References 7 publications

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“…Chadha and Madden [7] consider the numerical solution of a linear time dependent advection-diffusion problem by an implicit two-weight, three-point central finite difference scheme. They extend the scheme proposed by them in [8], to incorporate an optimal time step selection algorithm for the method. The resulting method, based on optimal values of weights and optimal time-stepping, is of fifth-order in space, and third-order in time.…”

Section: Introductionmentioning

confidence: 99%

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

Malheiro

Machado

Clain

2021

Computers & Mathematics with Applications

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Section: Introductionmentioning

confidence: 99%

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

Malheiro

Machado

Clain

2021

Computers & Mathematics with Applications

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An a posteriori strategy for adaptive schemes in time and space

Malheiro¹,

Machado²,

Clain³

2021

Preprint

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A nonlinear adaptive procedure for optimising both the schemes in time and space is proposed in view of increasing the numerical efficiency and reducing the computational time. The method is based on a four-parameter family of schemes we shall tune in function of the physical data (velocity, diffusion), the characteristic size in time and space, and the local regularity of the function leading to a nonlinear procedure. The a posteriori strategy we adopt consists in, given the solution at time t n , computing a candidate solution with the highest accurate schemes in time and space for all the nodes. Then, for the nodes that present some instabilities, both the schemes in time and space are modified and adapted in order to preserve the stability with a large time step. The updated solution is computed with node-dependent schemes both in time and space. For the sake of simplicity, only convection-diffusion problems are addressed as a prototype with a two-parameters five-points finite difference method for the spatial discretisation together with an explicit time two-parameters four-stages Runge-Kutta method. We prove that we manage to obtain an optimal time-step algorithm that produces accurate numerical approximations exempt of non-physical oscillations.

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A Two-Weight Scheme for a Time-Dependent Advection-Diffusion Problem

Cited by 2 publications

References 7 publications

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

An a posteriori strategy for adaptive schemes in time for one-dimensional advection-diffusion transport equations

An a posteriori strategy for adaptive schemes in time and space

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