scholarly journals ENHANCED MESHFREE RPIM WITH NURBS BASIS FUNCTION FOR ANALYSIS OF IRREGULAR BOUNDARY DOMAIN

2020 ◽  
Vol 32 (1) ◽  
Author(s):  
M.H. Mokhtaram ◽  
M.A. Mohd Noor ◽  
M.Z. Jamil Abd Nazir ◽  
A.R. Zainal Abidin ◽  
A.Y. Mohd Yassin
Keyword(s):  
Numerical Analysis ◽  
Interpolation Method ◽  
Order Approximation ◽  
Numerical Technique ◽  
Rational Approach ◽  
Irregular Domain ◽  
Essential Boundary Condition ◽  
Irregular Boundary ◽  
Stable Algorithm ◽  
Nurbs Basis Function

Radial Point Interpolation Method (RPIM) has become a powerful tool to numerical analysis due to its ability to provide a higher-order approximation function with the Kronecker delta property, by which the field nodes can be fitted exactly. However, one of the major drawbacks of RPIM is the inefficiency in handling irregular domain problems. This paper presents an enhanced RPIM formulation that employs Non-Uniform Rational B-Splines (NURBS) basis functions to represent the exact geometry of the boundary domain. The NURBS is a mathematical model which provides an efficient and numerically stable algorithm to exactly represent all conic sections in engineering modelling. Taking advantage of the flexibility and adaptivity of RPIM approximation and the accuracy of geometric representations by NURBS, this new method is able to improve geometry accuracy and flexibility in numerical analysis, thus providing a better and more rational approach to analyze irregular domain problems. Numerical problem of steady heat transfer considering curved beam is presented to verify the validity and accuracy of the developed method. The essential boundary condition can simply be imposed using direct imposition as in Finite Element Method (FEM). The result shows that the RPIM/NURBS achieved the converged solution much faster than conventional RPIM and FEM, with the number of nodes required only less than 200 for an error of less than 0.01%. This shows the potential of the developed method as a powerful numerical technique for future development.

Three-Dimensional Numerical Analysis of Transient Natural Convection in Rectangular Enclosures

1979 ◽  
Vol 101 (1) ◽  
pp. 114-119 ◽  
Author(s):  
A. M. C. Chan ◽  
S. Banerjee
Keyword(s):  
Porous Media ◽  
Natural Convection ◽  
Numerical Analysis ◽  
Turbulent Flows ◽  
Numerical Technique ◽  
Three Dimensional ◽  
Experimental Results ◽  
Primitive Form ◽  
Conservation Equations ◽  
Practical Utility

A simple numerical technique of considerable practical utility for the solution of transient multidimensional natural convection problems is described. It is based on the solution of the conservation equations in primitive form. The technique can be extended to calculation of natural convection problems in porous media and in turbulent flows where the eddy viscosities and conductivities can be predicted. It has been applied to the solution of several two and three-dimensional natural convection problems. The solutions compare well with the numerical and experimental results published by other investigators.

A MESHLESS METHOD ANALYSIS OF ELASTO-PLASTIC CONTACT PROBLEMS WITH FRICTION

2009 ◽  
Vol 01 (04) ◽  
pp. 631-645 ◽  
Author(s):  
ELHASSAN BOUDAIA ◽  
LAHBIB BOUSSHINE ◽  
GERY DE SAXCE ◽  
ALI CHAABA
Keyword(s):  
Numerical Analysis ◽  
Meshless Method ◽  
Plastic Material ◽  
Contact Problems ◽  
Transformation Method ◽  
Isotropic Hardening ◽  
Essential Boundary Condition ◽  
Theoretical And Numerical Analysis ◽  
Von Mises ◽  
Method Analysis

We present a theoretical and numerical analysis of incremental elasto-plastic problems based on the meshless method and the mathematical programming. This study is done on an elasto-plastic material with isotropic hardening obeying to the von Mises criterion. The transformation method is adopted to impose the essential boundary condition. The Coulomb's dry friction contact is used to implement the frictional boundary conditions and is formulated by the bipotential method which leads to only one principle of minimum in displacement. The numerical analysis results obtained by the method proposed in this paper are in good agreement with those obtained by FEM.

scholarly journals Design And Numerical Analysis of Morphing Airfoil With Corrugated Geometry In The Application MAV’s

2021 ◽  
Author(s):  
Kishore Kumar ◽  
Kanneti Nithisha ◽  
Manvi Vivek ◽  
Mohammad Saniya Simran ◽  
Ravi Sri Ra
Keyword(s):  
Reynolds Number ◽  
Numerical Analysis ◽  
Interpolation Method ◽  
Lower Surface ◽  
Aerodynamic Performance ◽  
Cartesian Grid ◽  
Computational Domain ◽  
Two Dimensional ◽  
Transient Nature ◽  
Turbulent Models

Abstract The main objective of the work is to enhance the aerodynamic performance during takeoff and cruise by using newly corrugated airfoil of MAV’s by Morphing it at the trailing edge. In this study, the transient nature of corrugated airfoils at low Reynolds number were assumed to be the flow is laminar, incompressible and two dimensional. The newly corrugated geometry which is parameterized from the camber line using a Radial basis function (RBF) based on interpolation method positioned at the lower surface of the airfoil i.e., NACA0015. Five morphed geometries are designed using ANSYS Space claimer. The computational domain is meshed using cartesian grid, the surface meshes with quadrilateral. Numerical simulations are performed with turbulent models i.e., k-omega, k-epsilon and Spalart allmaras. In the analysis, there is an increment of coefficient of lift and decrease in coefficient of drag by varying Reynolds number. Compared to NACA0015, corrugated NACA0015 shows good results.

Predicting Dynamic Behavior of Rotating Mindlin Plate Using Radial Point Interpolation Method

2019 ◽  
Vol 19 (07) ◽  
pp. 1950070 ◽  
Author(s):  
C. F. Du ◽  
D. G. Zhang ◽  
J. S. Zhang ◽  
J. H. Fan
Keyword(s):  
Dynamic Model ◽  
Interpolation Method ◽  
Order Approximation ◽  
Mindlin Plate ◽  
Radial Point Interpolation Method ◽  
Rotating Speed ◽  
Radial Point Interpolation ◽  
Point Interpolation Method ◽  
Point Interpolation ◽  
First Order Approximation

This paper proposes the radial point interpolation method (RPIM) for studying the dynamic behaviors of rotating Mindlin plates. By considering nonlinear coupling deformation, that is, the in-plane longitudinal shortening terms caused by transverse deformation, the first-order approximation coupled (FOAC) dynamic model is established using Lagrange’s equations of the second kind. The effectiveness of RPIM is first demonstrated in some static cases and then extended for dynamic analysis of a rectangular plate subjected to a large overall motion. The simulation results were compared with those obtained with zero-order approximation coupled (ZOAC) dynamic model, and it was observed that results obtained with FOAC dynamic model are more accurate, especially for cases involving high rotating speed. Furthermore, the influence of the radial basis shape parameters is discussed and the optimal parameters for plates are recommended. An approach to overcome the shear locking issue is also provided.

An Effective Finite Difference Method for Simulation of Bioheat Transfer in Irregular Tissues

2013 ◽  
Vol 135 (7) ◽  
Author(s):  
Zhi Zhu He ◽  
Xu Xue ◽  
Jing Liu
Keyword(s):  
Finite Difference ◽  
Finite Difference Method ◽  
Difference Method ◽  
Computational Cost ◽  
Adaptive Mesh ◽  
Bioheat Transfer ◽  
Large Temperature ◽  
Irregular Domain ◽  
Computational Accuracy ◽  
Irregular Boundary

A three-dimensional (3D) simulation of bioheat transfer is crucial to analyze the physiological processes and evaluate many therapeutic/diagnostic practices spanning from high to low temperature medicine. In this paper we develop an efficient numerical scheme for solving 3D transient bioheat transfer equations based on the alternating direction implicit finite-difference method (ADI-FDM). An algorithm is proposed to deal with the boundary condition for irregular domain which could capture accurately the complex boundary and reduce considerably the staircase effects. Furthermore, the local adaptive mesh technology is introduced to improve the computational accuracy for irregular boundary and the domains with large temperature gradient. The detailed modification to ADI-FDM is given to accommodate such special grid structure, in particular. Combination of adaptive-mesh technology and ADI-FDM could significantly improve the computational accuracy and decrease the computational cost. Extensive results of numerical experiments demonstrate that the algorithm developed in the current work is very effective to predict the temperature distribution during hyperthermia and cryosurgery. This work may play an important role in developing a computational planning tool for hyperthermia and cryosurgery in the near future.

scholarly journals Vibration analysis of the plate with the regular and irregular domain by using the Barycentric Lagrange interpolation

2018 ◽  
Vol 39 (3) ◽  
pp. 485-501
Author(s):  
Yen Liang Yeh
Keyword(s):  
Natural Frequency ◽  
Lagrange Interpolation ◽  
Interpolation Method ◽  
Three Dimensional ◽  
Regular Domain ◽  
Irregular Domain ◽  
Node Number ◽  
Dynamic Motion ◽  
Various Boundary Conditions ◽  
Multiple Dimensions

This paper uses the Barycentric Lagrange interpolation method to explore the free vibration of a plate with the regular and irregular domain using the Chebyshev function, allowing us to consider multiple dimensions. From our results, it can be shown that the Barycentric Lagrange interpolation method can solve three-dimensional problems. In the analysis, we can see that the Barycentric Lagrange interpolation method can solve the dynamic motion of the plate with regular domain, and the error of the simulation can be reduced to 0.15%. The effect of the geometric node number on the simulated error of the natural frequency of the plate is very profound. The Barycentric Lagrange interpolation method and the extrapolation difference method can solve the natural frequency of the plate with irregular domain. The error of the simulation on the natural frequency can be reduced to 1.084%. This allows us to understand the vibration of the plate with the regular and irregular domain under various boundary conditions quickly.

A Second Order Ghost Fluid Method for an Interface Problem of the Poisson Equation

2017 ◽  
Vol 22 (4) ◽  
pp. 965-996 ◽  
Author(s):  
Cheng Liu ◽  
Changhong Hu
Keyword(s):  
Linear System ◽  
Elliptic Equations ◽  
Order Approximation ◽  
Second Order ◽  
Iterative Solvers ◽  
Interface Problems ◽  
Interface Problem ◽  
Algebraic Equations ◽  
Irregular Domain ◽  
Ghost Fluid Method

AbstractA second order Ghost Fluid method is proposed for the treatment of interface problems of elliptic equations with discontinuous coefficients. By appropriate use of auxiliary virtual points, physical jump conditions are enforced at the interface. The signed distance function is used for the implicit description of irregular domain. With the additional unknowns, high order approximation considering the discontinuity can be built. To avoid the ill-conditioned matrix, the interpolation stencils are selected adaptively to balance the accuracy and the numerical stability. Additional equations containing the jump restrictions are assembled with the original discretized algebraic equations to form a new sparse linear system. Several Krylov iterative solvers are tested for the newly derived linear system. The results of a series of 1-D, 2-D tests show that the proposed method possesses second order accuracy in L∞ norm. Besides, the method can be extended to the 3-D problems straightforwardly. Numerical results reveal the present method is highly efficient and robust in dealing with the interface problems of elliptic equations.

Sign in / Sign up

Export Citation Format

Share Document