Solenoidal Field

Solenoidal Field

 

a vector field that has no source. In other words, the divergence of a vector a of a solenoidal field is equal to zero: div a = 0. An example of a solenoidal field is a magnetic field: div B = 0, where B is the magnetic induction vector. A solenoidal field can always be represented in the form a = curl b; here, curl is the differential operator also known as rotation, and the vector b is called the vector potential of the field. (See alsoVECTOR CALCULUS.)

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In semi-implicit algorithm, a projection onto the solenoidal field provides error clean-up in pressure field, while in explicit algorithm, re-initialization of density field to remove error accumulation is essential.
To attenuate errors of projection onto solenoidal field and resultant errors of volume conservation, the ECS (Error Compensating Source) of PPE was proposed for both MPS and ISPH methods (Khayyer and Gotoh, 2011).
Baseline concepts include the use of PMMs to remove the solenoidal field.