A Saulyev Explicit Scheme for an One-Dimensional Advection-Diffusion-Reaction Equation in an Opened Uniform Flow Stream

Pawarisa Samalerk, Nopparat Pochai

Abstract


The one-dimensional advection-diffusion-reaction equation is a mathematical model describing the transport and diffusion problems such as pollutants and suspended matter in a river or channel. If the velocity field is non-uniform the model cannot be theoretically manipulated, there for numerical techniques are required. The object of this research is to propose a simple advection-diffusion-reaction numerical simulation by using the Saulyev schemes. The proposed numerical technique uses an unconditionally stable method. It is the large or small of time step and/or grid size can be employed in the techniques. Among examples are calculated for three $\theta$ values. The case of $\theta = 0$ gives a smooth solution compare to the another values. Increasing the mass decay rate affects the maximum concentration level. The numerical experiments show that the calculated results are reasonable approximations.

Full Text: PDF

Refbacks

  • There are currently no refbacks.


The Thai Journal of Mathematics organized and supported by The Mathematical Association of Thailand and Thailand Research Council and the Center for Promotion of Mathematical Research of Thailand (CEPMART).

Copyright 2020 by the Mathematical Association of Thailand.

All rights reserve. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, without the prior permission of the Mathematical Association of Thailand.

|ISSN 1686-0209|