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. Balmus, Maximilian; Massing, André; Hoffman, Johan; Razavi, Reza; Nordsletten, David A.: A partition of unity approach to fluid mechanics and fluid-structure interaction (2020)
  2. Duan, Zhaowen; Wang, Z. J.: A high-order flux reconstruction method for 3D mixed overset meshes (2020)
  3. Hessenthaler, Andreas; Balmus, Maximilian; Röhrle, Oliver; Nordsletten, David: A class of analytic solutions for verification and convergence analysis of linear and nonlinear fluid-structure interaction algorithms (2020)
  4. Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.: Fourth-order accurate fractional-step IMEX schemes for the incompressible Navier-Stokes equations on moving overlapping grids (2020)
  5. Angel, Jordan B.; Banks, Jeffrey W.; Henshaw, William D.; Jenkinson, Michael J.; Kildishev, Alexander V.; Kovačič, Gregor; Prokopeva, Ludmila J.; Schwendeman, Donald W.: A high-order accurate scheme for Maxwell’s equations with a generalized dispersive material model (2019)
  6. Banks, Jeffrey W.; Odu, Andre Gianesini; Berger, Richard; Chapman, Thomas; Arrighi, William; Brunner, Stephan: High-order accurate conservative finite difference methods for Vlasov equations in 2D+2V (2019)
  7. Wachs, Anthony: Particle-scale computational approaches to model dry and saturated granular flows of non-Brownian, non-cohesive, and non-spherical rigid bodies (2019)
  8. 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)
  9. 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)
  10. Domino, Stefan P.: Design-order, non-conformal low-Mach fluid algorithms using a hybrid CVFEM/DG approach (2018)
  11. 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)
  12. 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)
  13. Batty, Christopher: A cell-centred finite volume method for the Poisson problem on non-graded quadtrees with second order accurate gradients (2017)
  14. Hu, Fangyuan; Matsunaga, Takuya; Tamai, Tasuku; Koshizuka, Seiichi: An ALE particle method using upwind interpolation (2017)
  15. Koblitz, A. R.; Lovett, S.; Nikiforakis, N.; Henshaw, W. D.: Direct numerical simulation of particulate flows with an overset grid method (2017)
  16. Meng, F.; Banks, J. W.; Henshaw, W. D.; Schwendeman, D. W.: A stable and accurate partitioned algorithm for conjugate heat transfer (2017)
  17. Allen, T.; Zerroukat, M.: A deep non-hydrostatic compressible atmospheric model on a Yin-Yang grid (2016)
  18. 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)
  19. Hayashi, Hiroshi; Kageyama, Akira: Yin-Yang-Zhong grid: an overset grid system for a sphere (2016)
  20. Kozdon, Jeremy E.; Wilcox, Lucas C.: Stable coupling of nonconforming, high-order finite difference methods (2016)

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