The reproducing kernel particle method for two-dimensional unsteady heat conduction problems

Cheng, Rongjun; Liew, K. M.
December 2009
Computational Mechanics;Dec2009, Vol. 45 Issue 1, p1
Academic Journal
The numerical solution to two-dimensional unsteady heat conduction problem is obtained using the reproducing kernel particle method (RKPM). A variational method is employed to furnish the discrete equations, and the essential boundary conditions are enforced by the penalty method. Convergence analysis and error estimation are discussed. Compared with the numerical methods based on mesh, the RKPM needs only the scattered nodes instead of meshing the domain of the problem. The effectiveness of the RKPM for two-dimensional unsteady heat conduction problems is examined by two numerical examples.


Related Articles

  • Uniform Pointwise Convergence of Difference Schemes for Convection-Diffusion Problems on Layer-Adapted Meshes. Kopteva, N. // Computing;2001, Vol. 66 Issue 2, p179 

    We consider two convection-diffusion boundary value problems in conservative form: for an ordinary differential equation and for a parabolic equation. Both the problems are discretized using a four-point second-order upwind space difference operator on arbitrary and layer-adapted space meshes....

  • An image-based modeling framework for patient-specific computational hemodynamics. Antiga, Luca; Piccinelli, Marina; Botti, Lorenzo; Ene-Iordache, Bogdan; Remuzzi, Andrea; Steinman, David A. // Medical & Biological Engineering & Computing;Nov2008, Vol. 46 Issue 11, p1097 

    We present a modeling framework designed for patient-specific computational hemodynamics to be performed in the context of large-scale studies. The framework takes advantage of the integration of image processing, geometric analysis and mesh generation techniques, with an accent on full...

  • Continuous and discrete parabolic operators and their qualitative properties. FARAG�, ISTV�N; HORV�TH, R�BERT // IMA Journal of Numerical Analysis;Jul2009, Vol. 29 Issue 3, p606 

    The basic requirement of numerical methods is convergence. However, from the practical point of view, it is generally not sufficient to construct convergent numerical methods for the solutions of partial differential equations. The qualitative adequateness of the methods is also an issue. The...

  • Generation of three-dimensional delaunay meshes from weakly structured and inconsistent data. Garanzha, V.; Kudryavtseva, L. // Computational Mathematics & Mathematical Physics;Mar2012, Vol. 52 Issue 3, p427 

    A method is proposed for the generation of three-dimensional tetrahedral meshes from incomplete, weakly structured, and inconsistent data describing a geometric model. The method is based on the construction of a piecewise smooth scalar function defining the body so that its boundary is the zero...

  • Application of the spherical metric tensor to grid adaptation and the solution of applied problems. Kofanov, A.; Liseikin, V.; Rychkov, A. // Computational Mathematics & Mathematical Physics;Apr2012, Vol. 52 Issue 4, p548 

    New results concerning the construction and application of adaptive numerical grids for solving applied problems are presented. The grid generation technique is based on the numerical solution of inverted Beltrami and diffusion equations for a monitor metric. The capabilities of the spherical...

  • A Conventional Approach for the Solution of the Fifth Order Boundary Value Problems Using Sixth Degree Spline Functions. Kalyani, Parcha; Rama Chandra Rao, Patibanda S.; Madhusudhan Rao, Ammiraju Sowbhagya // Applied Mathematics;Apr2013, Vol. 4 Issue 4, p583 

    In this communication we have used Bickley's method for the construction of a sixth order spline function and apply it to solve the linear fifth order differential equations of the form yv (x) + g (x) y (x) = r (x) where g (x) and r (x) are given functions with the two different problems of...

  • Local and parallel finite element algorithms for time-dependent convection-diffusion equations. Qing-fang Liu; Yan-ren Hou // Applied Mathematics & Mechanics;Jun2009, Vol. 30 Issue 6, p787 

    Local and parallel finite element algorithms based on two-grid discretization for the time-dependent convection-diffusion equations are presented. These algorithms are motivated by the observation that, for a solution to the convection-diffusion problem, low frequency components can be...

  • Adaptive Techniques for Spline Collocation. Christara, C.; Ng, Kit // Computing;Jan2006, Vol. 76 Issue 3/4, p259 

    We integrate optimal quadratic and cubic spline collocation methods for second-order two-point boundary value problems with adaptive grid techniques, and grid size and error estimators. Some adaptive grid techniques are based on the construction of a mapping function that maps uniform to...

  • MAXIMUM NORM ANALYSIS OF AN OVERLAPPING NONMATCHING GRIDS METHOD FOR THE OBSTACLE PROBLEM. Boulbrachene, M.; Saadi, S. // Advances in Difference Equations;2006, p1 

    We provide a maximum norm analysis of an overlapping Schwarz method on nonmatching grids for second-order elliptic obstacle problem. We consider a domain which is the union of two overlapping subdomains where each subdomain has its own independently generated grid. The grid points on the...


Read the Article


Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics