Development of an urban meteorological numerical model
In Cartesian coordinate
余偉明（Weiming Sha）
Geophysical Institute, Graduate School of Science, Tohoku University
Aoba-Ku, Sendai, 980-8578, Japan
Tel.: 022-217-5783; E-mail:sha@wind.geophys.tohoku.ac.jp
topography, i.e., the “shaved cell” approach,
1. Introduction
Since terrain-following vertical coordinate
and the numerical scheme for the equations
(sigma) system (Phillips 1957; Gal－Chen
of geophysical flows, in which the height is
and
used
used as vertical coordinate, have been
extensively to accommodate orography in
proposed (Adcroft et al. 1997; Marshall et al.
models for atmospheric flows, most of
1997; Bonaventura 2000). It is reasonable to
existing community meso-scale atmospheric
expect that a goal of running a regional
numerical model in the word are using the
model at a very high horizontal resolution
terrain-following coordinate as the vertical
may be attainable in the near future, and the
coordinate. However, a problem that has
topography and objects (e.g., buildings in
received
the
urban city) could be more accurately
development of sigma system primitive
represented. In such a situation, it seems
equation
the
natural to search for an alternative that will
noncancellation errors in the two terms of the
be better suited to handle the step topography
gradient force in the momentum equation
and complex objects on the surface for the
(Smagoringsky, et al. 1967). Mesinger and
high-resolution models currently used as well
Janjic(1985), among others, have found that
as a future model expected to run with a finer
errors in computing the horizontal pressure
resolution.
gradient force in models using a sigma
2.Concept of the numerical framework
coordinate can be substantial in the vicinity
In this numerical development, Finite
of steep topography. To minimize this error, a
Volume Method (FVM) in conjunction with
step-mountain
the
the SIMPLER (Semi-Implicit Method for
so-called “eta coordinate”, is implemented
Pressure-Linked Equation Revised; Patankar
in the National Centers for Environmental
1980) algorithms is used for calculations of
prediction
the
Somerville
1975)
attention
models
rather
is
vertical
(NCEP)
has
been
early
that
in
of
coordinate,
Meso
Eta
Model
unsteady,
three
dimensional,
(Mesinger et al. 1988) in which the
compressible Navier-Stokes equations on a
topography is represented as discrete steps
staggered grid. Abandoning the customary
(step mountain). Recently, representation of
terrain-following
normalization,
the
Cartesian coordinate, in which the height is
Comput. Phys., 17, 209-228.
used as the vertical one, is chose. A
(3) Smagorinsky, J., J.L.Holloway and G.D.
Cartesian-grid
Hembree, 1967, Proc. Inter. Symp. Dynamics
system
approach,
which
consists of the variable regular cells and a
Large Scale Atmospheric Processes, 70-134.
special treatment of the boundary cells, is
(4) Mesinger, F. and Z.I.Janjic, 1985, Large
proposed for expression of the arbitrarily
Scale Computations in Fluid Mechanics,
complex geometries. Blocking-off Method
Amer. Math. Soc., 81-120.
(Patankar 1980) is then introduced to handle
(5) Mesinger, F., S.Nickovic, D.Gavrilov and
the steep topography and complex objects
D.G.Deaven, 1988, Mon. Wea. Rev., 116,
above the Earth’s sea-level surface, thus
1493-1518.
resulting in a robust and efficient numerical
(6)Adcroft, A., C.Hill and J. Marshall, 1997,
scheme which allows for applications to
Mon., Wea. Rev., 125,2293-2315.
meso-scale flows over complex orography.
(7)
The spatial discretization is obtained by a
L.Perelman and C. Heisey, 1997, J. Geophys.,
finite volume technique on the staggered grid,
Res., 102, 5753-5766.
and higher-order upwind convection scheme
(8) Bonaventura, L., 2000, J. Comput. Phys.,
is employed to relate the flux at each control
158, 186-213.
volume face. For the temporal integration of
(9) Patankar, S.V., 1980, Numerical Heat and
the equation, the fully time implicit scheme is
Transfer and Fluid Flow.
Marshall,
J.,
A.Adcroft,
C..Hill,
utilized. As the fully implicit temporal
discretization is used，the time step can be
Fig. 1 Turbulent urban flow in Ootemati,
determined
Tokyo.
only
physical
criteria
and
accuracy considerations.
3. Some results of cases test
As a test, the model has been run on
calculating flows over cube/steep mountain by
Direct Numerical Simulation (DNS), and
turbulent flow in an urban city, i.e., Ootemati,
Tokyo (Fig.1) by Large Eddy Simulation (LES),
respectively. Detailed results will be presented
in the meeting.
4. Reference
(1) Phillips, N. A., 1957, J. Meteor. 14,
184-185.
(2) Gal-Chen, T., and R. Somerville, 1975, J.