Hybrid laplace transform/weighting function scheme for transient multidimensional conservation equations

✍ Scribed by Tzer-Ming Chen

• Book ID: 103931120
• Publisher: Elsevier Science
• Year: 1993
• Tongue: English
• Weight: 742 KB
• Volume: 26
• Category: Article
• ISSN: 0898-1221
• DOI: 10.1016/0898-1221(93)90056-2

✦ Synopsis

hybrid Laplace transform/weighting function scheme is developed for solving timedependent multidimensional conservation equations. The new method removes the time derivatives from the governing differential equations using the Laplace transform and solves the associated equation with the weighting function scheme. The similarity transform method is used to treat the complex coefficient system of the equations, which allows the simplest form of complex number functions to be obtained, and then to use the partial fractions method or a numerical method to invert the Laplace transform and transform the functions to the physical plane. Three different examples have been analyzed by the present method. The present method solutions are compared in tables with the exact solutions and those obtained by the other numerical methods. It is found that the present method is a reliable and efficient numerical tool.

TZER-MING CHEN

Subscript i Node number j Node number k Node number 2 In the z-direction Y In the y-direction z In the z-direction