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 :
- smoothed particle hydrodynamics, a Lagrangian method of solving fluid problems,
- Spectral methods, a technique where the equations are projected onto basis functions like the spherical harmonics and Chebyshev polynomials
- 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.
- The geometry (physical bounds) of the problem is defined.
- The volume occupied by the fluid is divided into discrete cells (the mesh).
- The physical modelling is defined - for example, the equations of motions + enthalpy + species conservation
- 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.
- The equations are solved iteratively as a steady-state or transient.
- Analysis and visualization of the resulting solution.
