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8  <meta content="Marcus Oliver Letzel" name="AUTHOR">
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19<h2 style="line-height: 100%;"><font size="4">2.0 Basic techniques of
20the LES model and its parallelization </font>
22<p style="line-height: 100%;">LES models generally permit the
23simulation of turbulent flows, whereby those eddies, that carry the
24main energy are resolved by the numerical grid. Only the
25effect of such turbulence elements with diameter equal to or smaller
26than the grid spacing are parameterized in the model and
27by so-called subgrid-scale (SGS) transport. Larger structures are
28simulated directly (they are explicitly resolved) and their effects are
29represented by the advection terms. </p>
30<p style="font-style: normal; line-height: 100%;">PALM is based on the
31non-hydrostatic incompressible Boussinesq equations. It contains a
32water cycle with cloud formation and takes into account infrared
33radiative cooling in cloudy conditions. The model has six prognostic
34quantities in total – u,v,w, liquid water potential temperature
35<font face="Thorndale, serif">&#920;</font><sub>l </sub>(BETTS,
361973), total water content q and subgrid-scale turbulent kinetic energy
37e. The
38subgrid-scale turbulence is modeled according to DEARDOFF (1980) and
39requires the solution of an additional prognostic equation for the
40turbulent kinetic energy e. The long wave radiation scheme is based
41on the parametrization of cloud effective emissivity (e.g. Cox, 1976)
42and condensation is considered by a simple '0%-or-100%'-scheme, which
43assumes that within each grid box the air is either entirely
44unsaturated or entirely saturated ( see e.g., CUIJPERS and DUYNKERKE,
451993). The water cycle is closed by using a simplified version of
46KESSLERs scheme (KESSLER, 1965; 1969) to parameterize precipitation
47processes (MÜLLER and CHLOND, 1996). Incompressibility is
48applied by means of a Poisson equation for pressure, which is solved
49with a direct method (SCHUMANN and SWEET, 1988). The Poisson equation
50is Fourier transformed in both horizontal directions and the
51resulting tridiagonal matrix is solved for the transformed pressure
52which is then transformed back. Alternatively, a multigrid method can
53also be used. Lateral boundary conditions of the model are cyclic and
54MONIN-OBUKHOV similarity is assumed between the surface and the first
55computational grid level above. Alternatively, noncyclic boundary
57(Dirichlet/Neumann) can be used along one of the
58horizontal directions. At the lower surface, either temperature/
59humidity or their respective fluxes can be prescribed. </p>
60<p style="font-style: normal; line-height: 100%;">The advection terms
61are treated by the scheme proposed by PIACSEK and WILLIAMS (1970),
62which conserves the integral of linear and quadratic quantities up to
63very small errors. The advection of scalar quantities can optionally
64be performed by the monotone, locally modified version of Botts
65advection scheme (CHLOND, 1994). The time integration is performed
66with the third-order Runge-Kutta scheme. A second-order Runge-Kutta
67scheme, a leapfrog scheme and an Euler scheme are also implemented.</p>
68<p style="line-height: 100%;">By default, the time step is computed
69with respect to the different criteria (CFL, diffusion) and adapted
70automatically. In case of a non-zero geostrophic
71wind the coordinate system can be moved along with the mean wind in
72order to maximize the time step (Galilei-Transformation). </p>
73<p style="font-style: normal; line-height: 100%;">In principle a model
74run is carried out in the following way: After reading the control
75parameters given by the user, all prognostic variables are
76initialized. Initial values can be e.g. vertical profiles of the
77horizontal wind, calculated using a 1D subset of the 3D prognostic
78equation and are set in the 3D-Model as horizontally homogeneous
79initial values. Temperature profiles can only be prescribed linear
80(with constant gradients, which may change for different vertical
81height intervals) and they are assumed in the 1D-Model as stationary.
82After the initialization phase during which also different kinds of
83disturbances may be imposed to the prognostic fields, the time
84integration begins. Here for each individual time step the prognostic
85equations are successively solved for the velocity components u, v and
87as well as for the potential temperature and possibly for the TKE.
88After the calculation of the boundary values in accordance with the
89given boundary conditions the provisional velocity fields are
90corrected with the help of the pressure solver. Following this, all
91diagnostic turbulence quantities including possible
92Prandtl-layer–quantities are computed. At the end of a time
93step the data output requested by the user is made
94(e.g. statistic of analyses for control purposes or profiles and/or
95graphics data). If the given end-time was reached, binary data maybe
96be saved for restart. </p>
97<p style="font-style: normal; line-height: 100%;">The model is based
98on the originally non-parallel LES model which has been operated at the
99institute since 1989
100and which was parallelized for massively parallel computers with
101distributed memory using the Message-Passing-Standard MPI. It is
102still applicable on a single processor and also well optimized for
103vector machines. The parallelization takes place via a so-called domain
104decomposition, which divides the entire model
105domain into individual, vertically standing cubes, which extend from
106the bottom to the top of the model domain. One processor (processing
107element, PE) is assigned to each cube, which
108accomplishes the computations on all grid points of the subdomain.
109Users can choose between a two- and a one-dimensional domain
110decomposition. A 1D-decomposition is preferred on machines with a
111slow&nbsp; network interconnection. In case of a 1D-decomposition, the
112grid points along x direction are
113distributed among the individual processors, but in y- and z-direction
114all respective grid points belong to the same PE. </p>
115<p style="line-height: 100%;">The calculation of central differences or
116non-local arithmetic operations (e.g. global
117sums, FFT) demands communication and an appropriate data exchange
118between the PEs. As a substantial innovation in relation to
119the non-parallel model version the individual subdomains are
120surrounded by so-called ghost points, which contain the grid point
121information of the neighbor processors. The appropriate grid point
122values must be exchanged after each change (i.e. in particular after
123each time step). For this purpose MPI routines (<tt>MPI_SENDRCV</tt>)
124are used. For the solution of the FFT conventional (non-parallelized)
125procedures are used. Given that the FFTs are used in x and/or
126y-direction, the data which lie distributed on the individual central
127processing elements, have to be collected and/or relocated before.
128This happens by means of the routine <tt>MPI_ALLTOALLV</tt>. Certain
129global operations like e.g. the search for absolute maxima or minima
130within the 3D-arrays likewise require the employment of special MPI
131routines (<tt>MPI_ALLREDUCE</tt>). </p>
132<p style="line-height: 100%;">Further details of the internal model
133structure are described in the <a href="../tec/index.html">technical/numerical
134documentation</a>. <br>
135&nbsp; </p>
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