Changes between Version 3 and Version 4 of doc/tec/lpm
- Timestamp:
- Jun 23, 2016 6:38:21 PM (9 years ago)
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doc/tec/lpm
v3 v4 54 54 \frac{9\,\nu\,\rho_0}{2\,r^2\,\rho_{\mathrm{p},0}}\,\cdot\,\left(1 + 55 55 0.15 \cdot {Re}_\mathrm{p}^{0.687} \right). 56 \label{eq:lpm2}57 56 \end{align*} 58 57 }}} … … 111 110 #!Latex 112 111 \begin{align*} 113 &114 \label{eq:LS5a}115 112 \tau_\mathrm{L} = \frac{4}{3}\frac{e}{c_{\text{sgs}} 116 113 C_\mathrm{L}\epsilon}\,, … … 118 115 }}} 119 116 which describes the time span during which ''u'',,p,,^sgs^''(t - Δt'',,L,,'')'' is correlated to ''u'',,p,,^sgs^''(t)''. The applied time step of the particle model hence must not be larger than τ,,L,,. In PALM, the particle time step is set to be smaller than ''τ'',,L,,'' / 40''. The second term on the right-hand side of the Eq. for d''u'',,p,i,,^sgs^ ensures that the assumption of well-mixed conditions by [#thomson1987 Thomson (1987)] is fulfilled on the subgrid scales. This term can be considered as drift correction, which shall prevent an over-proportional accumulation of particles in regions of weak turbulence (#rodean1996 Rodean, 1996). The third term on the right-hand side is of stochastic nature and describes the SGS diffusion of particles by a Gaussian random process. For a detailed derivation and discussion of 120 the Eq. for d''u'',,p,i,,^sgs^ see [#thomson1987 Thomson (1987)], [#rodean1996 Rodean (1996)] and [#weil2004 Weil et al. (2004) }.117 the Eq. for d''u'',,p,i,,^sgs^ see [#thomson1987 Thomson (1987)], [#rodean1996 Rodean (1996)] and [#weil2004 Weil et al. (2004)]. 121 118 122 119 The required values of the resolved-scale particle velocity components, ''e'', and ''ε'' are obtained from the respective LES fields using the eight adjacent grid points of the LES and tri-linear interpolation on the current particle location (see Sect. [wiki:/doc/tec/particle particle code structure]). An exception is made in case of no-slip boundary conditions set for the resolved-scale horizontal wind components below the first vertical grid level above the surface. Here, the resolved-scale particle velocities are determined from MOST (see … … 131 128 $\overline{w^{\prime\prime}v^{\prime\prime}}_0$ 132 129 }}} 133 are first bi-linearly interpolated to the horizontal location of the particle. In a second step the velocities are determined using the Eqs. for ''u'',,∗,,, ''∂u/∂z'' and ''∂v/∂z'' (\ref{eq:most:begin})--(\ref{eq:most:end}). Resolved-scale horizontal 134 velocities of particles residing at height levels below $z_0$ are set 135 to zero. The LPM allows to switch off the transport by the SGS 136 velocities. 130 are first bi-linearly interpolated to the horizontal location of the particle. In a second step the velocities are determined using the Eqs. for ''u'',,∗,,, ''∂u/∂z'' and ''∂v/∂z'' in Sect [wiki:/doc/tec/bc boundary conditions]. Resolved-scale horizontal velocities of particles residing at height levels below ''z'',,0,, are set to zero. The LPM allows to switch off the transport by the SGS velocities. 137 131 138 132 == Boundary conditions and release of particles ==
