One Approach to the Numerical Solution of Mass-Transfer Problems with Large Péclet Numbers

We consider a mathematical model of propagation of drugs in the wall of a vessel. The model is described by the advection-diffusion boundary-value problem with a system of two differential equations. In view of the specific features of the input parameters of the problem, when the advection coefficient significantly exceeds the diffusion coefficient, the application of the classical finite-element method with linear and quadratic basis functions leads to the loss of stability of the computational process. We propose a new approach to the solution of the advection-diffusion problems with large Péclet numbers based on the replacement of the unknown function by an exponential function in the formulation of the problem and the inverse replacement prior to the application of the finite-element method. We also perform the numerical analysis of the results obtained by the application of the proposed method for the approximate solution of the problem of propagation of drugs in the wall of a vessel.

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Correspondence to Yu. I. Turchyn.

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Translated from Matematychni Metody ta Fizyko-Mekhanichni Polya, Vol. 61, No. 2, pp. 150–158, April–June, 2018.

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Savula, Y.H., Turchyn, Y.I. One Approach to the Numerical Solution of Mass-Transfer Problems with Large Péclet Numbers. J Math Sci 253, 168–179 (2021). https://doi.org/10.1007/s10958-021-05221-9

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Keywords

  • advection-diffusion equation
  • finite-element method
  • loss of stability of the solution
  • Péclet number