  We introduce Semi-Implicit Lagrangian Voronoi Approximation (SILVA), a novel
numerical method for the solution of the incompressible Euler and Navier-Stokes
equations, which combines the efficiency of semi-implicit time marching schemes
with the robustness of time-dependent Voronoi tessellations. In SILVA, the
numerical solution is stored at particles, which move with the fluid velocity
and also play the role of the generators of the computational mesh. The Voronoi
mesh is rapidly regenerated at each time step, allowing large deformations with
topology changes. As opposed to the reconnection-based
Arbitrary-Lagrangian-Eulerian schemes, we need no remapping stage. A
semi-implicit scheme is devised in the context of moving Voronoi meshes to
project the velocity field onto a divergence-free manifold. We validate SILVA
by illustrative benchmarks, including viscous, inviscid, and multi-phase flows.
Compared to its closest competitor, the Incompressible Smoothed Particle
Hydrodynamics (ISPH) method, SILVA offers a sparser stiffness matrix and
facilitates the implementation of no-slip and free-slip boundary conditions.
