Chimera grids for water simulation

ABSTRACT

We introduce a new method for large scale water simulation using Chimera grid embedding, which discretizes space with overlapping Cartesian grids that translate and rotate in order to decompose the domain into different regions of interest with varying spatial resolutions. Grids can track both fluid features and solid objects, allowing for dynamic spatial adaptivity without remeshing or repartitioning the domain. We solve the inviscid incompressible Navier-Stokes equations with an arbitrary-Lagrangian-Eulerian style semi-Lagrangian advection scheme and a monolithic SPD Poisson solver. We modify the particle level set method in order to adapt it to Chimera grids including particle treatment across grid boundaries with disparate cell sizes, and strategies to deal with locality in the implementation of the level set and fast marching algorithms. We use a local Voronoi mesh construction to solve for pressure and address a number of issues that arise with the treatment of the velocity near the interface. The resulting method is highly scalable on distributed parallel architectures with minimal communication costs.

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Index Terms

• Computing methodologies

  • Computer graphics

    • Animation

      • Physical simulation

    • Shape modeling

• Mathematics of computing

  • Continuous mathematics

    • Topology

      • Geometric topology