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Computational fluid dynamics
The most fundamental consideration in CFD is how one treats a
continuous fluid in a discretized fashion on a computer. One method is
to discretize the spatial domain into small cells to form a volume
mesh or grid, and then apply a suitable algorithm to solve the
equations of motion (Euler equations for inviscid, and Navier-Stokes
equations for viscid flow). In addition, such a mesh can be either
irregular (for instance consisting of triangles in 2D, or pyramidal
solids in 3D) or regular; the distinguishing characteristic of the
former is that each cell must be stored separately in memory. Lastly,
if the problem is highly dynamic and occupies a wide range of scales,
the grid itself can be dynamically modified in time, as in adaptive
mesh refinement methods.
If one chooses not to proceed with a mesh-based
method, a number of alternatives exist, notably :
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smoothed particle hydrodynamics, a Lagrangian
method of solving fluid problems,
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Spectral methods, a technique where the
equations are projected onto basis functions like the spherical
harmonics and Chebyshev polynomials
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Lattice Boltzmann
methods, which simulate an equivalent mesoscopic system on
a Cartesian grid, instead of solving the macroscopic system (or
the real microscopic physics).
Methodology
In all of these approaches the same basic procedure
is followed.
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The geometry (physical bounds) of the problem
is defined.
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The volume occupied by the fluid is divided
into discrete cells (the mesh).
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The physical modelling is defined - for
example, the equations of motions + enthalpy + species
conservation
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Boundary conditions are defined. This involves
specifying the fluid behaviour and properties at the boundaries of
the problem. For transient problems, the initial conditions are
also defined.
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The equations are solved iteratively as a
steady-state or transient.
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Analysis and visualization of the resulting
solution
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