  A novel multi-resolution technique called border mapping multi-resolution
(BMMR) is proposed for projection-based particle methods. The BMMR aims to
obtain background equivalent particle distributions in the two sides of a
border between sub-domains with a 2:1 resolution ratio so that a single
resolution framework is adopted to near-border particles calculations. The
novelty of the BMMR is that it obtains the background grid from the mapping of
the actual particle distribution in the border and, as a result, the location
of the particles in the background grid exactly matches the location of the
actual particles. In this way, such technique aims to reduce the error from the
interpolation of the physical quantities in the background grid and to avoid
sudden changes in the particle distribution that may lead to unstable local
pressure calculation. In the coarse side of the border, the refinement is made
by a triangulation and by placing fictitious particles in the midpoints of the
triangles. In the fine side of the border, the derefinement is made by defining
a set of fine particles that result in a particle distribution that best
resembles a coarse one. The accuracy and computational performance of the BMMR
implemented in a moving particle semi-implicit (MPS) simulation system are
verified by using benchmark test cases of 2D free surface flows.
