Description
Return one second-order lattice-Boltzmann equilibrium population.
A simulation update combines supplied states, fluxes, forces and time conventions. Local integration and interface terms can be evaluated independently, while a full solver must also supply consistent fields, boundary conditions, conservation and convergence behavior.
Return one second-order lattice-Boltzmann equilibrium population.
When to use this tool
Use Lattice Boltzmann One Population Equilibrium when checking one explicitly supplied integration, flux or lattice-population contribution.
How to use the tool and how it works
- Enter density, weight, cDotU, speedSquared, soundSpeedSquared. Use the units and conventions below.
- Run the tool. Correct any format, range, or cross-field input error before interpreting the output.
- Read equilibrium. Use the output convention below.
Return one second-order lattice-Boltzmann equilibrium population. Require density, weight and speedSquared >= 0 and soundSpeedSquared > 0; equilibrium = w*rho*[1+cDotU/cs²+cDotU²/(2*cs⁴)-speedSquared/(2*cs²)].1
| Input field | Meaning and units | Accepted input |
|---|---|---|
| density | Density on the same physical and unit basis as the supplied reference or component; see the formula above. | Required. Finite number; minimum 0. |
| weight | Caller-supplied weight on the stated observation, model or allocation basis. | Required. Finite number; minimum 0. |
| cDotU | C Dot U | Required. Finite number. |
| speedSquared | Supplied |u|² in matching lattice velocity units, not a speed. | Required. Finite number; minimum 0. |
| soundSpeedSquared | Positive cs² in the same squared-velocity unit. | Required. Finite number; strictly above 0. |
| Output field | Interpretation | Returned shape |
|---|---|---|
| equilibrium | Equilibrium | Required. Finite number. |
{
"input": {
"density": 1,
"weight": 0.5,
"cDotU": 0,
"speedSquared": 0,
"soundSpeedSquared": 1
},
"output": {
"equilibrium": 0.5
}
}Limitations and assumptions
- Supplied moments must use consistent lattice units; negative outputs are not clipped and no complete equilibrium distribution or low-Mach validity is verified.
- Inputs must satisfy both the field types and the cross-field conditions above. Invalid input causes an error; a successful false flag or documented placeholder is a different result.
- Numeric calculations use binary floating point unless exact decimal-integer arithmetic is explicitly stated. No hidden measurement tolerance or decimal rounding is added; nonfinite or out-of-contract results are rejected. Numeric signed-zero results are exported as zero.
Alternative or Complementary methods
Use and validate the complete numerical method with its state initialization, boundary conditions and physical model for a reliable simulation.
References
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