docs:classes:flowfield

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The FlowField class represents vector-valued fields of the form

and also scalar and tensor fields with appropriate changes in the dimensionality of the coefficients.
The barred T function is a Chebyshev polynomial scaled to fit the domain y ∈ [a,b]. ^{1)} The spatial domain
of a FlowField is Ω = [0,Lx] x [a,b] x [0,Lz], with periodicity in x and z.

In channelflow programming, fields such as velocity, pressure, stress tensors, vorticity, etc. are stored as variables of type FlowField. The main functionality of the FlowField class is

- algebraic and differential operations, +/-, +=, ∇, ∇
^{2}, norms, inner products, etc. - transforming back and forth between spectral coefficients and gridpoint values
- serving as input to DNS algorithms, which map velocity fields forward in time: u(x,t) → u(x, t+Δt)
- setting and accessing scpetral coefficients and gridpoint values
- reading and writing to disk

FlowFields are initialized with gridsize and cellsize parameters, read from disk, or assigned from computations. Examples:

FlowField f; // null value, 0-d field on 0x0x0 grid FlowField u(Nx, Ny, Nz, Nd, Lx, Lz, a, b); // Nd-dim field on Nx x Ny x Nz grid, [0,Lx]x[a,b]x[0,Lz] FlowField g(Nx, Ny, Nz, Nd, 2, Lx, Lz, a, b); // Nd-dim 2-tensor FlowField h("h"); // read from file "h.ff" FlowField omega = curl(u);

Assume f,g,h etc. are FlowField variables with compatible cell and grid sizes. Examples of possible operations

f += g; // f = f + g f = curl(g); f = lapl(g); f = div(g); f = diff(g, j, n); // f_i = d^n g_i /dx_j f = grad(g); // f_ij = dg_i / dx_j f = cross(g,h); f *= 2.7; // f = 2.7*f Real c = L2IP(f,g); // L2 inner product of f,g Real n = L2Norm(u); Real D = dissipation(u); Real E = energy(u); Real I = wallshear(u);

The latter functions are defined as

FlowField transforms are a complicated subject –there are transforms in x,y, and z and implicit symmetries in complex spectral coefficients due to the real-valuedness of the field, for instance. This section outlines the bare essentials of transforms and data access methods. For further details see the Channelflow User Guide.

docs/classes/flowfield.1234813480.txt.gz · Last modified: 2009/02/16 11:44 by gibson