Introduction to Ocean Numerical Modeling 3 2 Numerical

Introduction to Ocean Numerical Modeling #3. 2 – Numerical aspects II : Practical Global model SSH Gildas Cambon, IRD/LOPS, France regional model SST gildas. cambon@ird. fr

Practical II PDF available at http: //stockage. univ-brest. fr/~cambon/asi 18/sess 1/practical_sess 1/2_advanced_lin_adv_diff/

A) Oscillation equation is Used to test the behavior of the temporal schemes. Go in 2_advanced_lin_adv_diff/ ; use the program oscillation. m How to use it ? • Edit oscillation. m • Edit and set the parameters • Choose a temporal • Lauch the oscillation equation integration • clear all ; close all ; oscillation(1, 2) ;

A) Oscillation equation Euler-forward and Leap-Frog time stepping have been implemented • Test them on the oscillation equation ? • Can you describe the main characteristics of these schemes ? The main disadvantage of the Leap-Frog schemes is to produce a numerical mode. • Can you illustrate this numerical mode • What are the technique used to reduce/damp this numerical mode ?

B) Heat equation • Choose a temporal and a spatial scheme • Lauch the advection equation integration : Go in 2_advanced_lin_adv_diff/ and use the program chaleur. m Ø clear all, close all ; phi_num=chaleur(1, 2) ; • Visualize the results Ø visu_movie(phi_num, 1) OR The program 1. Integrate the equation choosing clear all, close all ; phi_num=chaleur(1, 2) the temporal and spatial schemes 2. Do an animation to visualize the advection ? How to use it ? • Edit advection. m • Edit and set the parameters dx, dt, c and nu

B) Heat equation Euler-forward and Leap-Frog time stepping have been implemented Euler forward: • Test on the heat equation? • Can you describe its main characteristics of these 2 schemes ? • Can you do the stability analysis of this FTCS scheme ? • Do you think it is well suited for the vertical diffusion in the ocean The main disadvantage of the Leap-Frog schemes is to produce a numerical mode. • Can you illustrate this numerical mode • Can you explain the Asselin filter technique ? • What is the main drawback of it ?

C) Advection equation is Go in 2_advanced_lin_adv_diff/ and use the program advection. m How to use it ? • Edit advection. m • Edit and set the parameters dx, dt, c, • Choose a temporal and a spatial scheme • Lauch the advection equation integration : Ø clear all, close all ; phi_num=advection(1, 2) ; • Visualize the results The program Ø visu_movie(phi_num, 1) 1. Integrate the equation choosing the OR temporal and spatial schemes clear all, close all ; phi_num=advection(1, 2) ; 2. Do an animation to visualize the advection ?

C) Advection equation • Select an initial condition : Gaussian or square • Choose a finite difference for the time derivative (sugg: Euler forward in time) • Choose a finite difference scheme for the spatial derivative (sugg : Upwind in space) • Find the relation for • Define the algorithm and describe what happens ? • Can you establish a stability criteria using the Von Neuman analysis we present ?

C) Advection equation • Select a new time scheme : => Leap frog • What is the order of the scheme ? • Test several initial conditions with the leap-frog • Change the 1 rst order upwind spatial scheme to a centered one • What happen ?