A numerical model of the shallow water equations 20-11-2006 Guillaume Riflet [email_address] http ://www.mohid.com/hydrogroup

The context LEFT Mecânica dos meios contínuos - spring 2006 Responsible: Prof. Pedro Bicudo Tutor: Guillaume Riflet  tool Student: Ana Luísa Grilo Pinho  study and report

LEFT Mecânica dos meios contínuos - spring 2006

Responsible: Prof. Pedro Bicudo

Tutor: Guillaume Riflet  tool

Student: Ana Luísa Grilo Pinho  study and report

The system

Shallow water equations

Shallow water equations

The mesh Arakawa fully staggered regular C - grid

Arakawa fully staggered regular C - grid

The numerical scheme

The numerical scheme

The numerical scheme

The numerical scheme

The numerical scheme

The numerical scheme

The numerical scheme

The numerical scheme

filtering

Stability criteria

Boundary conditions SIMPLE DIRICHELET CONDITIONS AT THE BOUNDARY

Test-case Gaussian elevation

Gaussian elevation

Gaussian Elevation 31 x 31 grid points 10 m depth 10 m spatial increment 0.1 s time increment 0.2 m water level max initial elevation

31 x 31 grid points

10 m depth

10 m spatial increment

0.1 s time increment

0.2 m water level max initial elevation

Gaussian Elevation 31 x 31 grid points 10 m depth 10 m spatial increment 0.1 s time increment 0.2 m water level max initial elevation Inviscid, frictionless

31 x 31 grid points

10 m depth

10 m spatial increment

0.1 s time increment

0.2 m water level max initial elevation

Inviscid, frictionless

Geostrophic equilibrium

Geostrophic equilibrium 20 x 20 grid points 2 m depth 5000 m spatial increment

20 x 20 grid points

2 m depth

5000 m spatial increment

End Guillaume Riflet