Examples in FronTier

1. 2-D Examples

   Example00   Example01  Example02  Example03  Example04  Example05

   Example06   Example07  Example08  Example09  Example10  Example11

   Example12  Example13     Example14  Example15    Example16

2. 3-D Examples

   Example00-3d  Example01-3d  Example02-3d  Example03-3d

   Example04-3d  Example05-3d  Example06-3d

3. Parallel Computing Examples

   Para-test

AMS 528

I ) AMS528 Assignment I

Upwind scheme Lax_Friedrichs scheme Leap_Frog scheme Lax_Wendroff scheme MacCormack scheme

II ) AMS528 Assignment II

Problem 4

1.) Implicit Central Difference:

      1. R=0.8

         i,)  N=200    ii,) N=400    iii,) N=800    iv,) N=1600

      2. R=1.5

         i,)  N=200    ii,) N=400    iii,) N=800    iv,) N=1600

2.) Crank Nicolson Scheme:

      1. R=0.8

         i,)  N=200    ii,) N=400    iii,) N=800    iv,) N=1600

      2. R=1.5

         i,)  N=200    ii,) N=400    iii,) N=800    iv,) N=1600

Problem 5

1.) Lax Friedrichs Scheme (N=200)

     i.) R=0.1   ii.) R=0.2   iii.) R=0.5   iv.) R=0.9   v.) R=0.99

2.) Upwind Scheme (N=200)

     i.) R=0.1   ii.) R=0.2   iii.) R=0.5   iv.) R=0.9   v.) R=0.99   

  III ) AMS528 Assignment III

problem 1

  linear wave equation:

 1.) Godunov scheme

    i.)N=200  ii.)N=400  iii.)N=800  iv.)N=1600 v.) errors

 2.) Glimm scheme

    i.)N=200  ii.)N=400  iii.)N=800  iv.)N=1600 v.) errors

  Burgers equation:

 1.)Godunov scheme

    i.)N=200  ii.)N=400  iii.)N=800  iv.)N=1600

 2.) Glimm scheme

    i.)N=200  ii.)N=400  iii.)N=800  iv.)N=1600

problem 2

 1.)two-step Lax Wendroff with N=1600

 2.)one-step Lax Wendroff with N=1600

problem 3

 1.)Lax Friedrich scheme

   i.)N=200, errors  ii.)N=400, errors  

 iii.)N=800, errors  iv.)N=1600,errors

 2.)Lax Wendroff scheme

   i.)N=200, errors ii.)N=400, errors

 iii.)N=800, errors iv.)N=1600,errors 

problem 4

 1.)upwind       scheme for linear system

 2.)Lax Wendroff scheme for linear system

problem 5

 (a)Lax Wendroff scheme without dispersion for linear wave equations  

    i.)N=200  ii.)N=400  iii.)N=800  iv.)N=1600

 (b)Lax Wendroff scheme with dispersions for linear wave equations  

    i.)epi=0.01  ii.)epi=0.02  iii.)epi=0.04  iv.)epi=0.08  v.)epi=0.15

   vi.)epi=1/R-1=0.11 which is upwind scheme

  vii.)epi=1/(R*R)-1=0.23 which is Lax Friedrich scheme

 (c)the case of MacCormack scheme is the same to the case of Lax wendroff scheme for linear equations

    for the Crank-Nicolson scheme:

  i.)epi=0.01  ii.)epi=0.02  iii.)epi=0.04  iv.)epi=0.08  v.)epi=0.12

 vi.)epi=0.16   v.)epi=0.20

IV) Assignment 4

(4)(a)

      i) explicit central N=200  N=400  N=800 N=1600

     ii) implicit central N=200  N=400  N=800 N=1600

    iii) crank nicolson  N=200  N=400  N=800 N=1600

     iv) dufort frankel   N=200  N=400  N=800 N=1600

  (b)

      i) explicit central N=200  N=400  N=800 N=1600

     ii) implicit central N=200  N=400  N=800 N=1600

    iii) crank nicolson  N=200  N=400  N=800 N=1600

     iv) dufort frankel   N=200  N=400  N=800 N=1600

(5)

  (b)  N=200  N=400  N=800 N=1600 

  (c)  N=1600,theta=0.2,r=0.04+0.025*t    N=1600,theta=0.2,r=0.14-0.025*4

  (d)  N=1600,r=0.08,theta=0.01   N=1600,r=0.08,theta=0.5

(6)

mu = 0.001, mesh size = 100by100

mu = 0.01 , mesh size = 100by100

mu = 0.1,    mesh size = 100by100