2.2 Partial Differential Equations | 2.2 Partial Differential Equations | Unit 2: Numerical Methods for Partial Differential Equations | Computational Methods in Aerospace Engineering | Aeronautics and Astronautics

<Convection
2.2.1Conservation Laws in Integral and Differential Form
2.2.2One-Dimensional Burgers Equation
2.2.3Convection
2.2.4Characteristics for One-Dimensional Burgers Equation
2.2.5Diffusion
2.2.6Convection-Diffusion
2.2.7Linear Elasticity
>Diffusion

2.2.4 Characteristics for One-Dimensional Burgers' Equation

Consider the one-dimensional Burgers' equation 2.17. What is the equation for the characteristic?

\(\frac{dx}{dt}=u\)

\(\frac{dx}{dt}=2u\)

\(\frac{dx}{dt}=u^2\)

\(\frac{dx}{dt}=\frac{1}{2}u^2\)

Answer: Following the explanation above, we see that for the Burgers' equation, we can obtain \(\frac{dU}{dt}=0\) if we set \(\frac{dx}{dt}=u\), which gives the characteristic.