Dissertation > Excellent graduate degree dissertation topics show

A Jump Condition Capturing Scheme for Elliptic Interface Problems

Author: ZhouYuanYuan
Tutor: HuangYunQing;XuJianJun
School: Xiangtan University
Course: Computational Mathematics
Keywords: elliptic interface problem jump condition capturing scheme im-mersed interface method level set method finite difference method
CLC: O241.82
Type: Master's thesis
Year: 2011
Downloads: 28
Quote: 0
Read: Download Dissertation


The immersed interface method is general technique for solving differential equations with interface problems and now it is applied in various aspects of fluid dynamics. Interface problems usually lead to differential equations whose solutions and its derivatives have discontinuities or non-smoothness across some interface. Many differential equation numerical methods do not work efficiently for interface problems.In this paper the immersed interface method for solving elliptic interface prob-lems in 2D is extended to the situation when interface and jumps are implicitly provided by functions on the grid points in a neighborhood of the interface. The resulting scheme is particularly suitable for interface capturing methods such as the level set method. Formulations of the original immersed interface method are mod-ified for this implicit setting, including the interface jump relations, the algebraic equations for determining the coefficients of the finite difference scheme at irregular grid points and the correction terms. The local truncation error at grid points just adjacent to the interface is of first order. Since the interface is of co-dimension one, the global second order accuracy for the solution in maximum norm can be achieved, as demonstrated by numerical examples. It is easier to implement since standard Lagrange interpolation is used to compute the derivatives of the interface quantities.

Related Dissertations

  1. The Study on R-M Instability of the Material Interface in Gas-water Compressible Flow,O359.1
  2. Variational multiphase image segmentation model and Split Bregman iterative algorithm,TP391.41
  3. The surface geometry noise removal of non- local variational model,TP391.41
  4. Image Segmentation Based on Active Contour Models,TP391.41
  5. Three-dimensional Segmentation of Medical Image,TP391.41
  6. Study on Level Set Evolution Without Reinitialization,TP391.41
  7. Research on Level-set Methods for Moving Interfaces of Gas-water-solid,O35
  8. Active Contour Model and its Application and Research in Medical Endoscope Image Segmentation,TP391.41
  9. Studies on Medical Image Segmentation Based on Variational Level Set,TP391.41
  10. Algorithm Research on Image Coregistration of SAR,TN957.52
  11. Research on Multiphase Image Segmentation Method,TP391.41
  12. Numerical Solution for Two Classes Fractional Partial Differential Equation,O241.82
  13. Discussion on Seismic Modeling and Numerical Dispersion Correcting in Double-Phase Medium Based on Reformulated BISQ Model,P631.4
  14. The Numerical Methods for BURGERS Equation and Stability Analysis,O241.82
  15. Theoretical Study on the Electronic Properties in Semiconductor Quantum Wires and Quantum Dots,O471.1
  16. Two-dimensional fractional reaction diffusion equation finite difference method,O241.82
  17. Several Numerical Methods for American Option Pricing,F830.9
  18. Studies of the Numerical Simulation of the Water Quality and Quantity Transport under Sea Surface Water and Groundwater Interaction,P641
  19. Study on Face Tracking Algorithm Based on Improved Particle Filtering,TP391.41
  20. Covariance Region Descriptor and Energy Modeling Under Level Set Framework,TP391.41
  21. Distance learning in the distribution of matching snake model,TP391.41

CLC: > Mathematical sciences and chemical > Mathematics > Computational Mathematics > Numerical Analysis > The numerical solution of differential equations, integral equations > Numerical Solution of Partial Differential Equations
© 2012 www.DissertationTopic.Net  Mobile