Grid Generation Methods

1. Front Matter

   Pages i-xx

   PDF

2. General Considerations

   • Vladimir D. Liseikin

   Pages 1-46

3. Coordinate Transformations

   • Vladimir D. Liseikin

   Pages 47-85

4. Grid Quality Measures

   • Vladimir D. Liseikin

   Pages 87-125

5. Stretching Method

   • Vladimir D. Liseikin

   Pages 127-173

6. Algebraic Grid Generation

   • Vladimir D. Liseikin

   Pages 175-200

7. Grid Generation Through Differential Systems

   • Vladimir D. Liseikin

   Pages 201-253

8. Variational Methods

   • Vladimir D. Liseikin

   Pages 255-291

9. Curve and Surface Grid Methods

   • Vladimir D. Liseikin

   Pages 293-323

10. Comprehensive Method

    • Vladimir D. Liseikin

    Pages 325-383

11. Numerical Implementations of Comprehensive Grid Generators

    • Vladimir D. Liseikin

    Pages 385-419

12. Control of Grid Properties

    • Vladimir D. Liseikin

    Pages 421-448

13. Unstructured Methods

    • Vladimir D. Liseikin

    Pages 449-479

14. Applications of Adaptive Grids to Solution of Problems

    • Vladimir D. Liseikin

    Pages 481-526

15. Back Matter

    Pages 527-530

    PDF

This new edition provides a description of current developments relating to grid methods, grid codes, and their applications to actual problems. Grid generation methods are indispensable for the numerical solution of differential equations. Adaptive grid-mapping techniques, in particular, are the main focus and represent a promising tool to deal with systems with singularities. This 3rd edition includes three new chapters on numerical implementations (10), control of grid properties (11), and applications to mechanical, fluid, and plasma related problems (13). Also the other chapters have been updated including new topics, such as curvatures of discrete surfaces (3). Concise descriptions of hybrid mesh generation, drag and sweeping methods, parallel algorithms for mesh generation have been included too.
This new edition addresses a broad range of readers: students, researchers, and practitioners in applied mathematics, mechanics, engineering, physics and other areas of applications.

• adaptive grid
• drag meshing
• Beltrami equation
• structured grids
• unstructured grids
• Octree decomposition
• algebraic grid generation
• Christoffel symbols
• Mesh adaptation
• immersed boundary method
• Delaunay triangulation
• Dirichlet tessellation
• spectral element algorithm
• hybrid grids
• finite element method
• inverse matrix method
• mesh generation
• grid clustering
• inverted Beltrami
• stretched grid method

“Each chapter provides a thorough description of the background of the method under consideration, explains its properties, and makes clear for which type of problem it is suitable. Plenty of carefully designed instructive figures provide examples illustrating the methods’ features. … It is also likely to form an excellent foundation for designing a semester’s set of lectures for a course addressing graduate students.” (Kai Diethelm, Computing Reviews, April, 2018)​

• Institute of Computational Technologies, Russian Academy of Sciences Institute of Computational Technologies, Novosibirsk, Russia

  Vladimir D. Liseikin

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