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Numerical modeling of coupled fluid flow
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请填写真实有效的信息，以便工作人员联系您，我们为您严格保密。Numerical Modeling in Geodynamics: Success, Failure and Perspective
Title:Numerical Modeling in Geodynamics: Success, Failure and Perspective
Affiliation:AA(Geophysical Institute, Karlsruhe University, Hertzstr. 16, Karlsruhe, 76187 G IIEPT, RAS, Warshavskoye sh. 79-2, Moscow, 117556 Russian Federation )
Publication:American Geophysical Union, Fall Meeting 2005, abstract #T12A-08
Publication Date:12/2005
Keywords:0545 Modeling (4255), 3225 Numerical approximations and analysis (4260)
Bibliographic Code:
A real success in numerical modeling of dynamics of the Earth can be
achieved only by multidisciplinary research teams of experts in
geodynamics, applied and pure mathematics, and computer science. The
success in numerical modeling is based on the
following basic, but
simple, rules. (i)
People need simplicity most, but they understand
intricacies best (B. Pasternak, writer). Start from a simple numerical
model, which describes basic physical laws by a set of mathematical
equations, and move then to a complex model. Never start from a complex
model, because you cannot understand the contribution
of each term of
the equations to the modeled geophysical phenomenon. (ii) Study the
numerical methods behind your computer code. Otherwise it becomes
difficult to distinguish true and erroneous solutions to the geodynamic
problem, especially when your problem is complex enough. (iii) Test your
model versus analytical and asymptotic solutions, simple 2D and 3D model
examples. Develop benchmark analysis of different numerical codes and
compare numerical results with laboratory experiments. Remember that the
numerical tool you employ is not perfect, and there are small bugs in
every computer code. Therefore the testing is the most important part of
your numerical modeling. (iv) Prove (if possible) or learn relevant
statements concerning the existence, uniqueness and stability of the
solution to the mathematical and discrete problems. Otherwise you can
solve an improperly-posed problem, and the results of the modeling will
be far from the true solution of your model problem. (v) Try to analyze
numerical models of a geological phenomenon using as less as possible
tuning model variables. Already two tuning variables give enough
possibilities to constrain your model well enough with respect to
observations. The data fitting sometimes is quite attractive and can
take you far from a principal aim of your numerical modeling: to
understand geophysical phenomena. (vi) If the number of tuning model
variables are greater than two, test carefully the effect of each of the
variables on the modeled phenomenon. Remember:
With four exponents I
can fit an elephant (E. Fermi, physicist). (vii) Make your numerical
model as accurate as possible, but never put the aim to reach a great
Undue precision of computations is the first symptom of
mathematical illiteracy (N. Krylov, mathematician). How complex should
be a numerical model?
A model which images any detail of the reality is
as useful as a map of scale 1:1 (J. Robinson, economist). This message
is quite important for geoscientists, who study numerical models of
complex geodynamical processes. I believe that geoscientists will never
create a model of the real Earth dynamics, but we should try to model
the dynamics such a way to simulate basic geophysical processes and
phenomena. Does a particular model have a predictive power? Each
numerical model has a predictive power, otherwise the model is useless.
The predictability of the model varies with its complexity. Remember
that a solution to the numerical model is an approximate solution to the
equations, which have been chosen in believe that they describe dynamic
processes of the Earth. Hence a numerical model predicts dynamics of the
Earth as well as the mathematical equations describe this dynamics. What
methodological advances are
still needed for testable geodynamic
modeling? Inverse (time-reverse) numerical modeling and data
assimilation are new methodologies in geodynamics. The inverse modeling
can allow to test geodynamic models forward in time using
(from present-day observations) initial conditions instead of
conditions.
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arXiv e-printsNumerical Simulation:Its Contributions to Turbulence Modeling.
Numerical Simulation:Its Contributions to Turbulence Modeling.
[文献类型]:科技报告[标题]:Numerical Simulation:Its Contributions to Turbulence Modeling.[作者]:ferziger, j. h.[机构]:Stanford Univ.,CA.*National Aeronautics and Space Administration,Washington,DC.[关键词]:compressible flow,shear flow,turbulence models,vortices,turbulent flow,computational fluid dynamics,reynolds stress,vorticity equations,[出版年份]:1992[报告时间]:Mar 92,[页码]:35p[馆藏索取号]:N92-24537[总页数]:36
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