SSP_Tools includes an interactive shell that quickly allows some operations and tests to be performed on the various numerical methods and example problems included in the toolkit. This interactive shell may be invoked by running TestSuite.m from the MATLAB interpreter.
[1] Animation
[2] Simple Approximation
[3] Convergence Test - ODE
[4] Convergence Test - PDE
[5] Positivity Test
[6] SSP Test
Select a Test:
Vector of refinements, e.g. [10,30,80] refinements:
Value of t to approximate to t [1]:
[1] Advection Equation u_t - a*u_x = 0
[2] Buckley-Leverett Equation
[3] Burgers Equation u_t - (1/2*u)_x = 0
[4] Convection-Advection Equation u_t + u_x + (0.5*u^2)_x = 0
[5] Convection-Reaction Equation u_t + \xi_1(0.5u)_x = \xi_2u
[6] Convection-Reaction Equation u_t + \xi_1u_x = \xi_2u^2
[7] Time Dependent PDE u_t = e(t) u.^2
Select a test problem:
Wavespeed Coefficient a [1]:
Select Initial Condition:
[1] sin(pi*x)
[2] 1/4 + sin(pi*x)
[3] Squarewave 1.0 (x<=0.5)
[4] Step Function [-1,1]
[5] Elevated Sinwave [-1, 1] u(0) = 1 + sin(pi*x)
Selection:
Configure Flux Discretizer:
[1] FiniteDifference
[2] KorenLimiter
[3] Spectral
[4] WenoCore
Select a discretizer:
Configuration options
[1] weno5
[2] weno9
[3] weno11
[4] weno13
[5] weno15
Weno Kernel kernel [weno5]:
smoothness parameter epsilon [1e-16]:
other smoothness parameter p [2]:
Configure Integrator for General Problem
[1] BackwardEuler
[2] LNL
[3] MSRK
[4] ODE23S
[5] ODE45
[6] RK3
[7] RK4
[8] RK5
[9] RK7
[10] RK8
[11] SSP104
[12] SSPRK
Select an integrator:
Now that the problem and numerical methods have been configured, the test will run.
PDE Convergence Test
Problem: < SSP_Tools.TestProblems.Advection: @(x)sin(pi*x) [-1, 1] t= >
Time Stepping Method: < SSP_Tools.Integrators.RK3 >
Spatial Discretization: < SSP_Tools.Discretizers.WenoCore: call=@WenoCore.weno_basic kernel=@WenoCore.kernels.weno5 epsilon=1e-16 p=2 >
Testing 10
Testing 20
Testing 30
Testing 40
Testing 50
Testing 60
Testing 70
Testing 80
Testing 90
Testing 100
Convergence Test Results
Problem: Advection Equation u_t - 1*u_x = 0 u(x,0)=@(x)sin(pi*x) T=1.000000
Spatial Discretization: WENO5 epsilon=1e-16 p=2
Time-Stepping Method: RK3
----------------------------------------------------
N | dt | L1Error | L1Order | L2Error | L2Order | LinfError | LinfOrder |
10 | 0.0400 | 1.60e-02 | - | 1.78e-02 | - | 2.97e-02 | - |
20 | 0.0200 | 7.51e-04 | 4.42 | 8.78e-04 | 4.34 | 1.48e-03 | 4.32 |
30 | 0.0133 | 9.85e-05 | 5.01 | 1.18e-04 | 4.94 | 2.07e-04 | 4.85 |
40 | 0.0100 | 2.45e-05 | 4.84 | 2.89e-05 | 4.90 | 4.95e-05 | 4.97 |
50 | 0.0080 | 8.50e-06 | 4.74 | 9.90e-06 | 4.81 | 1.75e-05 | 4.67 |
60 | 0.0067 | 3.65e-06 | 4.63 | 4.20e-06 | 4.70 | 7.37e-06 | 4.73 |
70 | 0.0057 | 1.82e-06 | 4.52 | 2.08e-06 | 4.58 | 3.54e-06 | 4.76 |
80 | 0.0050 | 1.01e-06 | 4.41 | 1.14e-06 | 4.46 | 1.97e-06 | 4.39 |
90 | 0.0044 | 6.07e-07 | 4.31 | 6.86e-07 | 4.35 | 1.15e-06 | 4.60 |
100 | 0.0040 | 3.90e-07 | 4.20 | 4.39e-07 | 4.24 | 7.34e-07 | 4.22 |