Department of Aerospace Engineering

Departmental Seminar: Dr. Hong-Sen Kou, "Adaptive Parameter Scheme in Solving the Problems of One-Dimensional Advection-Diffusion Equation and Two Dimensional Advection Equation Based on the Higher-Order Generalization of Taylor Series Expansion."

Hong-Sen Kou, Professor, Tatung University, Taiwan (Department of Mechanical Engineering), will be presenting a seminar at 10:00 AM on July 24, 2008 in Room 1235 Howe Hall.  A reception will be held following the presentation.

Adaptive Parameter Scheme in Solving the Problems of One-Dimensional Advection-Diffusion Equation and Two-Dimensional Advection Equation Based on the Higher-Order Generalization of Taylor Series Expansion

The beam element and plate bending element have been extensively utilized by the finite element method to calculate the transverse displacement and slopes (rotations) about the beam and the plate. These elements can keep a smooth distribution of the displacement on the nodes and hence they are usually adopted in the problems of the beam and plate to get higher accuracy.

Taylor’s series expansion can be expected as a useful approach to formulate the finite difference equation because this approach may monitor and control the order of truncation error via suitable manipulation. This speech introduces a general approach of the Taylor’s series expansion to derive a differential equation into the finite difference equations including the primitive variable associated with its first derivative. Since the merit of this method is similar to the beam element used in finite element method, good accuracy can be obtained especially in hyperbolic equation. Moreover, higher order approximation can be formulated by adjusting the adaptive parameters to obtain higher order of accuracy.

The finite difference equations in solving one-dimensional advection-diffusion equation and two-dimensional advection equation have been formulated with respect to their order of accuracy. Several examples are demonstrated to validate their efficacy. It is believed that solving the unknowns including the primitive variable associated with its first derivative simultaneously will be a potential approach to acquire the higher accuracy in the area of computational fluid dynamics. Therefore, the present approach is worthwhile for more exploration.