Description
Book SynopsisNumerical Methods for Atmospheric and Oceanic Sciences caters to the needs of students of atmospheric and oceanic sciences in senior undergraduate and graduate courses as well as students of applied mathematics, mechanical and aerospace engineering. The book covers fundamental theoretical aspects of the various numerical methods that will help both students and teachers in gaining a better understanding of the effectiveness and rigour of these methods. Extensive applications of the finite difference methods used in the processes involving advection, barotropic, shallow water, baroclinic, oscillation and decay are covered in detail. Special emphasis is given to advanced numerical methods such as Semi-Lagrangian, Spectral, Finite Element and Finite Volume methods. Each chapter includes various exercises including Python codes that will enable students to develop the codes and compare the numerical solutions obtained through different numerical methods.
Table of Contents1. Partial Differential Equations; 2. Equations of fluid motion; 3. Finite Difference Method; 4. Consistency and Stability Analysis; 5. Oscillation Decay Equations; 6. Linear Advection Equation; 7. Numerical Solution of Elliptic Partial Differential Equation; 8. Shallow Water Equations; 9. Numerical Methods for Solving Shallow Water Equations; 10. Numerical Methods for Solving Barotropic Equations; 11. Numerical Methods for Solving Baroclinic Equations; 12. Boundary Conditions; 13. Lagrangian and Semi-Lagrangian Schemes; 14. Spectral Methods; 15. Finite Volume and Finite Element Methods; 16. Ocean Models; A Tridiagonal Matrix Algorithm; Bibliography.
