We present a family of schemes for the approximation of one dimensional convection-diffusion equations. It is based on a linearization technique that allows to treat explicitly the hyperbolic term and linearly implicitly the parabolic one. This avoids the parabolic stability constraint of explicit schemes, and does not require any non-linear solver for the implicit problem. We present several numerical simulations to show the effectiveness of the proposed schemes and to investigate their stability, convergence and accuracy. In particular, since the proposed schemes provide to be accurate for both smooth and non-smooth solutions, they turn out to be attractive for adaptivity

Cavalli, F., Linearly implicit schemes for convection-diffusion equations, in Hyperbolic Problems: Theory, Numerics, Applications, (PADOVA -- ITA, 25-29 June 2012), AIMS, N/A 2013: 423-431 [http://hdl.handle.net/10807/85479]

Linearly implicit schemes for convection-diffusion equations

Cavalli
2013

Abstract

We present a family of schemes for the approximation of one dimensional convection-diffusion equations. It is based on a linearization technique that allows to treat explicitly the hyperbolic term and linearly implicitly the parabolic one. This avoids the parabolic stability constraint of explicit schemes, and does not require any non-linear solver for the implicit problem. We present several numerical simulations to show the effectiveness of the proposed schemes and to investigate their stability, convergence and accuracy. In particular, since the proposed schemes provide to be accurate for both smooth and non-smooth solutions, they turn out to be attractive for adaptivity
Inglese
Hyperbolic Problems: Theory, Numerics, Applications
International Conference on Hyperbolic Problems
PADOVA -- ITA
25-giu-2012
29-giu-2012
978-1-60133-017-8
AIMS
Cavalli, F., Linearly implicit schemes for convection-diffusion equations, in Hyperbolic Problems: Theory, Numerics, Applications, (PADOVA -- ITA, 25-29 June 2012), AIMS, N/A 2013: 423-431 [http://hdl.handle.net/10807/85479]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10807/85479
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