Divergence‐constrained moving least squares for fluid simulation

Abstract

Developing suitable interpolation methods to simulate dynamic motions of continuous materials such as fluids is an important problem. In this paper, we propose a novel method to enforce the divergence condition to the interpolated velocity field by moving least squares, by means of the diffusive derivatives and moving divergence constraints that allow the practical use and easy implementation. As results, we present the velocity interpolation examples and a fluid-like particle simulation method to show the meaningful potential of our method as a tool of physical interpolation for fluid simulations.

Strain-based diffusion solver for realistic representation of diffusion front in physical reactions

“…Some researchers [ 23 , 24 ] have suggested generating a fluid-like motion in an Eulerian framework without solving the Poisson equation. Instead, they create a divergence-constrained vector field u vel using a moving least-squares fitting process.…”

Visualization of Vector Fields from Density Data Using Moving Least Squares Based on Monte Carlo Method

“…Divergenceconstrained MLS [6] Figure 1: Comparing standard MLS vector interpolation to pseudodivergence-free vector interpolation [6].…”

Targeted smoke simulation combining control and turbulent flow

“…Other more sophisticated choices for interpolating velocity from sparse data in clude methods which are inherently divergence-free, a very attractive property for fluid simulation. Hong and Yoon describe a divergence-free method of interpolat ing velocity th at gives fluid-like results without using the Navier-Stokes equations at all [26], using moving least squares. By using diffusive derivatives and moving diver gence constraints, they achieve fluid-like interpolation, solving a moving least squares problem at every grid cell.…”