Composite overlapping meshes for the solution of partial differential equations. It is shown how to generate curvilinear overlapping grids and the numerical solution of partial differential equations on them. First, an overview of grid generation methods is presented. After defining the composite overlapping grid term, it is explained that the continuity conditions are imposed at the overlapping boundaries. For creating a composite grid with any number of component grids, the grid construction program CMPGRD is used. An analysis of the composite grid output and data structure is also presented. Some techniques for solving elliptic and time-dependent partial differential equations on composite meshes are shown. Applications to the solution of the compressible Navier-Stokes equations are discussed. Numerical accuracy, efficiency and the numerical solution are analyzed too together with some conclusions.

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  1. Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.: High-order upwind schemes for the wave equation on overlapping grids: Maxwell’s equations in second-order form (2018)
  2. de Laborderie, J.; Duchaine, F.; Gicquel, L.; Vermorel, O.; Wang, G.; Moreau, S.: Numerical analysis of a high-order unstructured overset grid method for compressible LES of turbomachinery (2018)
  3. Domino, Stefan P.: Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach (2018)
  4. Feng, Wenqiang; Guo, Zhenlin; Lowengrub, John S.; Wise, Steven M.: A mass-conservative adaptive FAS multigrid solver for cell-centered finite difference methods on block-structured, locally-Cartesian grids (2018)
  5. Tang, H. S.; Dong, W. B.; Agrawal, A.: A phenomenon of artificial odd-even grid oscillation and its presence in domain decomposition computation: algebraic analysis and numerical illustration (2018)
  6. Batty, Christopher: A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients (2017)
  7. Hu, Fangyuan; Matsunaga, Takuya; Tamai, Tasuku; Koshizuka, Seiichi: An ALE particle method using upwind interpolation (2017)
  8. Koblitz, A. R.; Lovett, S.; Nikiforakis, N.; Henshaw, W. D.: Direct numerical simulation of particulate flows with an overset grid method (2017)
  9. Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.: A stable and accurate partitioned algorithm for conjugate heat transfer (2017)
  10. Allen, T.; Zerroukat, M.: A deep non-hydrostatic compressible atmospheric model on a Yin-Yang grid (2016)
  11. Banks, J. W.; Henshaw, W. D.; Kapila, A. K.; Schwendeman, D. W.: An added-mass partition algorithm for fluid-structure interactions of compressible fluids and nonlinear solids (2016)
  12. Hayashi, Hiroshi; Kageyama, Akira: Yin-Yang-Zhong grid: an overset grid system for a sphere (2016)
  13. Kozdon, Jeremy E.; Wilcox, Lucas C.: Stable coupling of nonconforming, high-order finite difference methods (2016)
  14. Li, L.; Henshaw, W. D.; Banks, J. W.; Schwendeman, D. W.; Main, A.: A stable partitioned FSI algorithm for incompressible flow and deforming beams (2016)
  15. Lu, Jianfang; Fang, Jinwei; Tan, Sirui; Shu, Chi-Wang; Zhang, Mengping: Inverse Lax-Wendroff procedure for numerical boundary conditions of convection-diffusion equations (2016)
  16. Marrone, S.; Di Mascio, A.; Le Touzé, D.: Coupling of smoothed particle hydrodynamics with finite volume method for free-surface flows (2016)
  17. Merrill, Brandon E.; Peet, Yulia T.; Fischer, Paul F.; Lottes, James W.: A spectrally accurate method for overlapping grid solution of incompressible Navier-Stokes equations (2016)
  18. Shu, Chi-Wang: High order WENO and DG methods for time-dependent convection-dominated PDEs: A brief survey of several recent developments (2016)
  19. Petersson, N. Anders; Sjögreen, Björn: Wave propagation in anisotropic elastic materials and curvilinear coordinates using a summation-by-parts finite difference method (2015)
  20. Zerroukat, M.; Allen, T.: On the monotonic and conservative transport on overset/Yin-Yang grids (2015)

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