96
4. Finite DifTerence Methods
4.6. Use the subroutine developed in Exercise 4.4 to observe numerical
dispersion and overshoot errors (when the implicit scheme is used, let
V = 1, llX = 5, llt = 0.1. Systematically change the value of D L from 10
to 0.01).
4.7. When the explicit scheme (4.1.11) is used to solve the one-dimensional
problem (4.1.9), find the restrictions on llx and llt such that the scheme
is convergent and the numerical dispersion is less than 10% of the
physical dispersion.
4.8. Derive the two-dimensional numerical dispersion terms given in Eq.
(4.1.37).
4.9. Write the solution procedure of the method of characteristics (MOC)
step by step.
4.10. What are the differences between the MOC and the Random-Walk
method?
4.11. Present the key steps of using the Random-Walk method to solve
three-dimensional advection-dispersion problems.
4.12. When the Random-Walk method is used to solve an advection-dispersion problem, how can the radioactive decay and adsorption be taken
into account?
4. Finite DifTerence Methods
4.6. Use the subroutine developed in Exercise 4.4 to observe numerical
dispersion and overshoot errors (when the implicit scheme is used, let
V = 1, llX = 5, llt = 0.1. Systematically change the value of D L from 10
to 0.01).
4.7. When the explicit scheme (4.1.11) is used to solve the one-dimensional
problem (4.1.9), find the restrictions on llx and llt such that the scheme
is convergent and the numerical dispersion is less than 10% of the
physical dispersion.
4.8. Derive the two-dimensional numerical dispersion terms given in Eq.
(4.1.37).
4.9. Write the solution procedure of the method of characteristics (MOC)
step by step.
4.10. What are the differences between the MOC and the Random-Walk
method?
4.11. Present the key steps of using the Random-Walk method to solve
three-dimensional advection-dispersion problems.
4.12. When the Random-Walk method is used to solve an advection-dispersion problem, how can the radioactive decay and adsorption be taken
into account?