Animations for the fluid dynamics report

Index

1. Simple Advection Equation, constant velocity
2. Check Order of Convergence
3. Advection Equation, velocity = displacement
4. Burgers Equation
5. Fluid Equations, Primitive Reconstruction, Primitive Averaging
6. Fluid Equations, Conservative Reconstruction, Primitive Averaging
7. Fluid Equations, Primitive Reconstruction, Conservative Averaging
8. Fluid Equations, Conservative Reconstruction, Conservative Averaging

Simple Advection Equation, constant velocity

Piecewise constant reconstruction

• Euler
• Second Order Runge-Kutta
• Third Order Runge-Kutta

Piecewise linear reconstruction

• Euler
• Second Order Runge-Kutta
• Third Order Runge-Kutta

Naive reconstruction

• Euler
• Second Oder Runge-Kutta
• Third Order Runge-Kutta

Compare Evolution Types

• Euler
• Piecewise constant reconstruction
• Piecewise linear reconstruction
• Naive reconstruction

Check Order of Convergence

Euler evolution

• Euler
• Piecewise constant reconstruction, O(h)
• Piecewise constant reconstruction, O(h^2)
• Piecewise linear reconstruction, O(h)
• Piecewise linear reconstruction, O(h^2)

Second Order Runge-Kutta

• Euler
• Piecewise constant reconstruction, O(h)
• Piecewise constant reconstruction, O(h^2)
• Piecewise linear reconstruction, O(h)
• Piecewise linear reconstruction, O(h^2)

Third Order Runge-Kutta

• Euler
• Piecewise constant reconstruction, O(h)
• Piecewise constant reconstruction, O(h^2)
• Piecewise linear reconstruction, O(h)
• Piecewise linear reconstruction, O(h^2)
• Order of convergence test for piecewise linear reconstruction, magnified, O(h^2)
• Order of convergence test for piecewise linear reconstruction, magnified, O(h^2)

Advection Equation, velocity = displacement

Piecewise Constant

• Euler
• Euler
• Second order Runge-Kutta
• Third Order Runge-Kutta

Piecewise Linear

• Euler
• Euler
• Second Order Runge-Kutta
• Third Order Runge-Kutta

Naive

• Euler
• Euler
• Second Order Runge-Kutta
• Third Order Runge-Kutta

Compare all evolution types

• Euler
• Piecewise constant reconstruction
• Piecewise linear reconstruction
• Naive reconstruction

Burgers Equation

Gaussian Initial Data

• Euler
• Burger Roe Approximation
• Burger Exact Flux Calculation

Pulse Type A

• Euler
• A Roe
• A Exact

Pulse Type B

• Euler
• B Roe
• B Exact

Pulse Type C

• Euler
• C Roe
• C Exact

Triangular Initial Data

• Euler
• Exact
• Roe
• Exact Flux

Convergence Tests

• Euler
• Burger Convergence test -h Gaussain Initial Data
• Burger Convergence test merged with original waveform
• Burger Convergence test - h^2
• Burger convergence test - h Step function initial data
• Burger Convergence test - h^2 Step function initial data

Fluid Equations, Primitive Reconstruction, Primitive Averaging

Parameter Set A

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set B

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Paramter Set C

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Fluid Equations, Conservative Reconstruction, Primitive Averaging

Parameter Set A

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set B

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set C

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Fluid Equations, Primitive Reconstruction, Conservative Averaging

Parameter Set A

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set B

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set C

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Fluid Equations, Conservative Reconstruction, Conservative Averaging

Parameter Set A

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set B

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution

Parameter Set C

• Euler
• Fluid Density Evolution
• Fluid Velocity Evolution
• Fluid Pressure Evolution