The one-dimensional heat equation ut + a²uxx = 0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation u²+¹ _ un n+1 At • Comment on the linearity, order and type of the partial differential equation. • Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. = a² u+1-2u+u-1 4x² Using the modified equation method, investigate the stability of the discrete equation. Comment on any stability limitations in terms of choice of At. Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

The one-dimensional heat equation ut + a²uxx = 0 is discretised using the forward Euler time scheme and a two node centred spatial scheme. This discretisation results in the following equation u²+¹ _ un n+1 At • Comment on the linearity, order and type of the partial differential equation. • Check the consistency of the discrete equation and state the order of the truncation error for At and Ax. = a² u+1-2u+u-1 4x² Using the modified equation method, investigate the stability of the discrete equation. Comment on any stability limitations in terms of choice of At. Comment on the implications of this scheme with regards to numerical diffusion and dispersion, if any.

Principles of Heat Transfer (Activate Learning with these NEW titles from Engineering!)

8th Edition

ISBN:9781305387102

Author:Kreith, Frank; Manglik, Raj M.

Publisher:Kreith, Frank; Manglik, Raj M.

Chapter4: Numerical Analysis Of Heat Conduction

Section: Chapter Questions

Problem 4.21P

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