Two-Dimensional Adaptive Mesh Generation Algorithm and its Application with Higher-Order Compressible Flow Solver

Phongthanapanich, Sutthisak,Dechaumphai, Pramote The Korean Society of Mechanical Engineers 2004 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.18 No.12

A combined procedure for two-dimensional Delaunay mesh generation algorithm and an adaptive remeshing technique with higher-order compressible flow solver is presented. A pseudo-code procedure is described for the adaptive remeshing technique. The flux-difference splitting scheme with a modified multidimensional dissipation for high-speed compressible flow analysis on unstructured meshes is proposed. The scheme eliminates nonphysical flow solutions such as the spurious bump of the carbuncle phenomenon observed from the bow shock of the flow over a blunt body and the oscillation in the odd-even grid perturbation in a straight duct for the Quirk's odd-even decoupling test. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. The performance of the combined procedure is evaluated on unstructured triangular meshes by solving several steady-state and transient high-speed compressible flow problems.

J-integral calculation by domain integral technique using adaptive finite element method

Phongthanapanich, Sutthisak,Potjananapasiri, Kobsak,Dechaumphai, Pramote Techno-Press 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.4

An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near crack tips. The domain integral technique, for which all relevant quantities are integrated over any arbitrary element areas around the crack tips, is utilized as the J-integral solution scheme with 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure onto a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Several benchmark problems are analyzed to evaluate the efficiency of the combined domain integral technique and the adaptive finite element method.

Nodeless Variable Finite Element Mothod for Stress Analysis Using Flux-based Formulation

Sutthisak Phongthanapanich,Pramote Dechaumphai 대한기계학회 2008 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.22 No.4

A nodeless variable element is combined with an adaptive meshing technique to improve solution accuracy of the finite element method for analyzing two-dimensional elasticity problems. The nodeless variable element employs quadratic interpolation functions to provide higher solution accuracy without requiring additional actual nodes. The fluxbased formulation is developed for the nodeless variable finite element to reduce the complexity in deriving the finite element equations as compared to the conventional finite element method. The superconvergent patch recovery procedure is implemented to compute accurate stresses from the nodeless variable finite element solutions. The effectiveness of the combined procedure for providing higher solution convergence rate from the proposed formulation is evaluated by two well-known examples.

J-integral calculation by domain integral technique using adaptive finite element method

Sutthisak Phongthanapanich,Kobsak Potjananapasiri,Pramote Dechaumphai 국제구조공학회 2008 Structural Engineering and Mechanics, An Int'l Jou Vol.28 No.4

An adaptive finite element method for analyzing two-dimensional and axisymmetric nonlinear elastic fracture mechanics problems with cracks is presented. The J-integral is used as a parameter to characterize the severity of stresses and deformation near crack tips. The domain integral technique, for which all relevant quantities are integrated over any arbitrary element areas around the crack tips, is utilized as the J-integral solution scheme with 9-node degenerated crack tip elements. The solution accuracy is further improved by incorporating an error estimation procedure onto a remeshing algorithm with a solution mapping scheme to resume the analysis at a particular load level after the adaptive remeshing technique has been applied. Several benchmark problems are analyzed to evaluate the efficiency of the combined domain integral technique and the adaptive finite element method.

Combined finite volume and finite element method for convection-diffusion-reaction equation

Sutthisak Phongthanapanich,Pramote Dechaumphai 대한기계학회 2009 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.23 No.3

A combined finite volume and finite element method is presented for solving the unsteady scalar convectiondiffusion-reaction equation in two dimensions. The finite volume method is used to discretize the convection-diffusionreaction equation. The higher-order reconstruction of unknown quantities at the cell faces is determined by Taylor's series expansion. To arrive at an explicit scheme, the temporal derivative term is estimated by employing the idea of local expansion of unknown along the characteristics. The concept of the finite element technique is applied to determine the gradient quantities at the cell faces. Robustness and accuracy of the method are evaluated by using available analytical and numerical solutions of the two-dimensional pure-convection, convection-diffusion and convectiondiffusion-reaction problems. Numerical test cases have shown that the method does not require any artificial diffusion to improve the solution stability.

Two-Dimensional Adaptive Mesh Generation Algorithm and its Application with Higher-Order Compressible Flow Solver

Sutthisak Phongthanapanich,Pramote Dechaumphai 대한기계학회 2004 JOURNAL OF MECHANICAL SCIENCE AND TECHNOLOGY Vol.18 No.12

A combined procedure for two-dimensional Delaunay mesh generation algorithm and an adaptive remeshing technique with higher-order compressible flow solver is presented. A pseudo-code procedure is described for the adaptive remeshing technique. The flux-difference splitting scheme with a modified multidimensional dissipation for high-speed compressible flow analysis on unstructured meshes is proposed. The scheme eliminates nonphysical flow solutions such as the spurious bump of the carbuncle phenomenon observed from the bow shock of the flow over a blunt body and the oscillation in the odd-even grid perturbation in a straight duct for the Quirk's odd-even decoupling test. The proposed scheme is further extended to achieve higher-order spatial and temporal solution accuracy. The performance of the combined procedure is evaluated on unstructured triangular meshes by solving several steady-state and transient high-speed compressible flow problems.<br/>

Adaptive finite elements by Delaunay triangulation for fracture analysis of cracks

Dechaumphai, Pramote,Phongthanapanich, Sutthisak,Bhandhubanyong, Paritud Techno-Press 2003 Structural Engineering and Mechanics, An Int'l Jou Vol.15 No.5

Delaunay triangulation is combined with an adaptive finite element method for analysis of two-dimensional crack propagation problems. The content includes detailed descriptions of the proposed procedure which consists of the Delaunay triangulation algorithm and an adaptive remeshing technique. The adaptive remeshing technique generates small elements around the crack tips and large elements in the other regions. Three examples for predicting the stress intensity factors of a center cracked plate, a compact tension specimen, a single edge cracked plate under mixed-mode loading, and an example for simulating crack growth behavior in a single edge cracked plate with holes, are used to evaluate the effectiveness of the procedure. These examples demonstrate that the proposed procedure can improve solution accuracy as well as reduce total number of unknowns and computational time.

An efficient adaptive finite element method based on EBE-PCG iterative solver for LEFM analysis

Manat Hearunyakij,Sutthisak Phongthanapanich 국제구조공학회 2022 Structural Engineering and Mechanics, An Int'l Jou Vol.83 No.3

Linear Elastic Fracture Mechanics (LEFM) has been developed by applying stress analysis to determine the stress intensity factor (SIF, K). The finite element method (FEM) is widely used as a standard tool for evaluating the SIF for various crack configurations. The prediction accuracy can be achieved by applying an adaptive Delaunay triangulation combined with a FEM. The solution can be solved using either direct or iterative solvers. This work adopts the element-by-element preconditioned conjugate gradient (EBE-PCG) iterative solver into an adaptive FEM to solve the solution to heal problem size constraints that exist when direct solution techniques are applied. It can avoid the formation of a global stiffness matrix of a finite element model. Several numerical experiments reveal that the present method is simple, fast, and efficient compared to conventional sparse direct solvers. The optimum convergence criterion for two-dimensional LEFM analysis is studied. In this paper, four sample problems of a two-edge cracked plate, a center cracked plate, a single-edge cracked plate, and a compact tension specimen is used to evaluate the accuracy of the prediction of the SIF values. Finally, the efficiency of the present iterative solver is summarized by comparing the computational time for all cases.