Preface 1. Introduction 2. Conservation laws and differential equations 3. Characteristics and Riemann problems for linear hyperbolic equations 4. Finite-volume methods 5. Introduction to the CLAWPACK software 6. High resolution methods 7. Boundary conditions and ghost cells 8. Convergence, accuracy, and stability 9. Variable-coefficient linear equations 10. Other approaches to high resolution 11. Nonlinear scalar conservation laws 12. Finite-volume methods for nonlinear scalar conservation laws 13. Nonlinear systems of conservation laws 14. Gas dynamics and the Euler equations 15. Finite-volume methods for nonlinear systems 16. Some nonclassical hyperbolic problems 17. Source terms and balance laws 18. Multidimensional hyperbolic problems 19. Multidimensional numerical methods 20. Multidimensional scalar equations 21. Multidimensional systems 22. Elastic waves 23. Finite-volume methods on quadrilateral grids Bibliography Index.

https://depts.washington.edu/clawpack/book2/sample.pdf

Finite Volume Methods for Hyperbolic Problems

An efficient ghost-cell immersed boundary method (GCIBM) for simulating turbulent flows in complex geometries is presented. A boundary condition is enforced through a ghost cell method. The reconstruction procedure allows systematic development of numerical schemes for treating the immersed boundary while preserving the overall second-order accuracy of the base solver. Both Dirichlet and Neumann boundary conditions can be treated. The current ghost cell treatment is both suitable for staggered and non-staggered Cartesian grids. The accuracy of the current method is validated using flow past a circular cylinder and large eddy simulation of turbulent flow over a wavy surface. Numerical results are compared with experimental data and boundary-fitted grid results. The method is further extended to an existing ocean model (MITGCM) to simulate geophysical flow over a three-dimensional bump. The method is easily implemented as evidenced by our use of several existing codes.

A Ghost-Cell Immersed Boundary Method for Flow in Complex Geometry

SWASH: An operational public domain code for simulating wave fields and rapidly varied flows in coastal waters

The surface gradient method for the treatment of source terms in the shallow-water equations

https://personal.egr.uri.edu/grilli/shi_etal_om_2012.pdf

A high-order adaptive time-stepping TVD solver for Boussinesq modeling of breaking waves and coastal inundation

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

A high-resolution time-marching method is presented for solving the two-dimensional shallow water equations. The method uses a cell-centered formulation with collocated data rather than a space-staggered approach. Spurious oscillations are avoided by employing Monotonic Upstream Schemes for Conservation Laws (MUSCL) reconstruction with an approximate Riemann solver in a two-step Runge-Kutta time stepping scheme. A finite-volume implementation on a boundary conforming mesh is chosen to more accurately map the complex geometries that will occur in practice. These features enable the model to deal with dam break phenomena involving flow discontinuities, subcritical and supercritical flows, and other cases. The method is applied to several bore wave propagation and dam break problems.

High-resolution finite-volume method for shallow water flows

Developments in Cartesian cut cell methods

http://directory.umm.ac.id/Data%20Elmu/jurnal/A/Advances%20In%20Water%20Resources/Vol23.Issue5.2000/299.pdf

Clive G. Mingham

Papers

The surface gradient method for the treatment of source terms in the shallow-water equations

Numerical simulation of wave overtopping of coastal structures using the non-linear shallow water equations

High-resolution finite-volume method for shallow water flows

Developments in Cartesian cut cell methods

Calculation of shallow water flows using a Cartesian cut cell approach