Abstract

This study thoroughly explains the process of implementing Adaptive Mesh Refinement into a Finite Element Analysis program. Using the error norm, a routine for improving an original mesh for an arbitrary 2D structural problem has been developed. By utilizing user-defined relative global error, an optimal mesh for a given level of approximation can be obtained in an iterative manner. The routine (called AMG v1.0) runs with the pre-/postprocessor GiD and the calculation module Calsef, but can easily be tailored to work with other FEA programs. AMG operates with two mesh optimality criteria, which have proven to refine the mesh in a non-oscillatory manner. The open structure, along with the Graphical User Interface, makes AMG suitable for educational and experimental purposes. For validation, six examples within the field of structural engineering have been solved, four of which have been compared favorably with analytical solutions.

The mesh optimality routines used are general, why AMG can be extended to handle more types of elements, 3D analysis, and to be applicable to other types of engineering problems. Above all AMG serves as a first step of implementing Adaptive Mesh Refinement procedures into GiD.

Abstract

In this paper, numerical demonstrations of a modified compressible Euler system are shown, where the bubble function element stabilization method together with adaptive mesh refinement is introduced for increasing numerical stability and numerical accuracy. For a test case, NACA0012 is selected as a domain of interest, and numerical results using finite elements of P1­P1b­P1 and P2­P2b­P2 for density­velocity­pressure were compared at AOA=1.25 and Mach number 0.8. As a result, the shock wave is not found on the upper­end and the lower­ end of NACA0012 in the former, and on the other hand the latter is adequate numerical result and relative errors of Cl, Cd with previous study are 1.197% and 0.15376%. The mathematical model is much simpler than the compressible Euler equation, because they are advection equations for a density, a velocity, and a pressure with each external forces. Therefore, the material derivative is considered for time stepping, and the characteristic curve method can be used for decreasing calculation cost.