Mack and I are working on designing a way to limit the values of the interpolation function derived from the particles for a given property in a given cell. The simplest example, which is our test case, is the ‘Beam’ property from the Bending Beam benchmark with particles. The property Beam = 1 if the particle lies within the beam at time t = 0 and Beam = 0 otherwise. In this computation the values for Beam on the particles are *constant* for the entire computation. During the course of the Bending Beam computation the Bilinear Least Squares (BLS) interpolation algorithm will overshoot and undershoot, i.e., have values > 1 and < 0 respectively, as will the Quadratic Least Squares (QLS) interpolation algorithm.

My question is a simple one. Prior to placing the new interpolated values for Beam on the support points of the compositional field associated with the property ‘Beam’ at the new time t^{n+1}, are the values on that computational field still the values for Beam at time t^n; i.e., from the nth time step? Our limiting strategy needs the value of Beam at some point on the cell (e.g., the center) or perhaps the average value of Beam over the cell at the previous time step.

Another way to phrase my question is "Does the compositional field associated with Beam retain the values of Beam from the previous time step, *the same way that* uold retains the values of the velocity at the previous time step?