Poisson Equation

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Poisson Equation

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1. The partial differential equation

Missing Image:img src="SP7_p_files/del.gif"²Missing Image:img src="SP7_p_files/phisms.gif" = F

where Missing Image:img src="SP7_p_files/del.gif"² is the Laplacian operator; Missing Image:img src="SP7_p_files/phisms.gif" a scalar function of position; and F is a given function of the independent space variables. For the special case F = 0, the Poisson equation reduces to the Laplace equation. See relaxation method. </dd>
2. The relationship between the temperature T and pressure p of a perfect gas undergoing an adiabatic

process; given by T = constant X p^μ

where μ is the Poisson constant. </dd>
This equation defines a family of process lines, called isentropes or dry adiabats, each of which represents the changes of state possible in a fluid with a constant value of entropy. </dd>

References

This article is based on NASA's Dictionary of Technical Terms for Aerospace Use