6.11 A Note on Grid Size
Due to computer memory restrictions the grid size Δλ and the corresponding timestep interval Δτ had to be increased in order to generate plots covering a larger
overall time interval τ corresponding to the later stages of the expansion. This was
necessary as maintaining Δλ and Δτ at their origin values (as used for the early stages
of the spherical expansion) required the use of a considerably larger number of timesteps in the numerical procedure. Attempts to implement this increased number
resulted in the program terminating with the statement “not enough memory for
this operation”. Unfortunately, the need to increase the grid size resulted in larger
oscillations and the spreading of the shock front over a similar number of grid
intervals but having somewhat larger grid size.
6.12 Conclusions
In Sect. 6.10 we considered the sudden expansion of a high-pressure, high-temperature sphere into the atmosphere by numerically integrating the difference equations
with artificial viscosity included. Plots of pressure, particle velocity and density were
presented as a function of normalized Lagrangian radius at various time intervals
during the spherical expansion. It should be noted that Chou and Huang [6] have also
investigated the spherical symmetric flow from a high-pressure sphere that is
Normalized Radius
Fig. 6.19 Particle velocity as a function of normalized radius is shown during the later stages of the
expansion of the isothermal sphere at the times indicated. For the numerical procedure the following
parameters apply; Δλ ¼ 0.00914, λ s ¼ 0.0457,κ ¼ 1.2, Δτ ¼ 1.2 Â 10
À4 and γ ¼ 1.4
6.12 Conclusions
311
Due to computer memory restrictions the grid size Δλ and the corresponding timestep interval Δτ had to be increased in order to generate plots covering a larger
overall time interval τ corresponding to the later stages of the expansion. This was
necessary as maintaining Δλ and Δτ at their origin values (as used for the early stages
of the spherical expansion) required the use of a considerably larger number of timesteps in the numerical procedure. Attempts to implement this increased number
resulted in the program terminating with the statement “not enough memory for
this operation”. Unfortunately, the need to increase the grid size resulted in larger
oscillations and the spreading of the shock front over a similar number of grid
intervals but having somewhat larger grid size.
6.12 Conclusions
In Sect. 6.10 we considered the sudden expansion of a high-pressure, high-temperature sphere into the atmosphere by numerically integrating the difference equations
with artificial viscosity included. Plots of pressure, particle velocity and density were
presented as a function of normalized Lagrangian radius at various time intervals
during the spherical expansion. It should be noted that Chou and Huang [6] have also
investigated the spherical symmetric flow from a high-pressure sphere that is
Normalized Radius
Fig. 6.19 Particle velocity as a function of normalized radius is shown during the later stages of the
expansion of the isothermal sphere at the times indicated. For the numerical procedure the following
parameters apply; Δλ ¼ 0.00914, λ s ¼ 0.0457,κ ¼ 1.2, Δτ ¼ 1.2 Â 10
À4 and γ ¼ 1.4
6.12 Conclusions
311