Comprarar el efecto del látex de papaya en diferentes concentraciones en el reblandecimiento del cálculo supragingival en pacientes de la consulta

Peruse and Petra each contain a number of computational settings whose values need to be chosen to avoid influencing the temperature distributions. Settings that were found to have a negligible effect include the option to retain partial densities for mixtures, a function to remove small volume fractions of material left behind during advection, the default maximum value of four Lagrangian steps per Eulerian remap step in Petra, and cutoffs to prevent numerical rounding errors causing motion in cells that should be at rest. The settings that were found to have a significant effect on the results are discussed below. Timestep settings

The timestep used to advance the numerical solution in Peruse and Petra is controlled by the Courant factor (see section2.2.1). In addition, an initial timestep can be specified by the user and timestep growth factors control the rate at which the timestep can change. Within appropriate ranges, it was found that the choice of values for the timestep controls has very little effect on the temperature distributions, demonstrating that the results are timestep-converged. A Courant factor of 0.2 in Petra and 0.5 in Peruse has been used for all the simulations described in this chapter, with an initial timestep of 10−5µs and

a growth factor of 2.0 in Petra. The reasons why the two codes need different Courant factors is currently under investigation [110].

Artificial viscosity

The Wilkins form [98] of artificial viscosity is commonly used in Petra while a mono- tonic artificial viscosity [27] is recommended in situations where there is a suspicion of artificial viscosity over-heating, and this can either use an estimate of the sound speed or the actual value calculated from the equation of state. Monotonic artificial viscosity is also available in Peruse. Changing the artificial viscosity treatment was found to have a slight effect on the temperature distributions, but it is small compared to the variation that occurs as a function of time (figure7.2). For consistency between Peruse and Petra, the monotonic artificial viscosity option with sound speed calculated from the equation of state and coefficientsβL =0.5,βQ= 0.75 has been used in this chapter.

Pressure relaxation and energy dissipation

Pressure relaxation is available in Petra to allow the materials within a mixed cell to ap- proach pressure equilibrium at the end of the Lagrangian step (see section 2.2.1). As shown in figure7.4, pressure relaxation makes a bigger difference to the binder temper- ature distribution than to that of HMX, because the small proportion of binder in the plastic-bonded explosive means that much of it is located in mixed cells. Since pressure relaxation is designed to improve the accuracy of the numerical solution, it is switched on in the Petra calculations described in this chapter.

An energy dissipation function is available in Petra to add the kinetic energy lost from each cell during advection to its internal energy, similar to that implemented in Chec. The effect of using energy dissipation is shown in figure7.5. When dissipation is turned off, the temperatures reached in the simulation are lower than when it is turned on because energy has been lost. Since it helps conserve total energy, energy dissipation is turned on for the simulations in this chapter.

Pressure relaxation and energy dissipation are not applicable to Peruse which is a Lagrangian code with no advection step and no mixed cells.

Figure 7.4: Effect of pressure relaxation in a Petra type C calculation. Pressure relaxation is switched on for the other simulations in this chapter.

Figure 7.5: Effect of energy dissipation in a Petra type C calculation. Energy dissipation is switched on for the other simulations in this chapter.

Boundary conditions

Type A, B and C calculations in Petra use a reflective boundary as a rigid wall at the bottom of the computational geometry, as illustrated in figure7.1, with several rows of void cells and a transmissive boundary at the top. The void cells are included to allow inflow through the transmissive boundary at the top of the computational domain. It was checked that the choice of either transmissive or reflective lateral boundary conditions at the left and right of the domain makes very little difference to the resulting temperature distributions, so reflective lateral boundaries are used. The effect of introducing an initial gap between the explosive microstructure and the rigid wall in a type C Petra calcula- tion was found to be much smaller than the variation that occurs as a function of time (figure7.2), so the majority of the simulations in this chapter have no gap.

In Peruse, a reflective boundary is used as a rigid wall with a free surface at the other end of the computational geometry. It was found that the temperature distributions ob- tained using a rigid-wall boundary or a symmetrical-impact geometry are almost identical.