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James Shaw edited this page Oct 24, 2017 · 8 revisions

High-order finite volume transport for arbitrary polyhedral meshes

  • Motivation
    • horizontal meshes: triangular icosahedra, hexagonal icosahedra, cubed sphere
    • vertical meshes: cut cell and slanted cell meshes have a mix of hexahedra, triangular prisms, pentagonal prisms ✅
    • OLAM uses triangular icosahedra with cut cells ✅
  • Terminology
    • structured, unstructured, arbitrary/hybrid (sometimes also simply called 'unstructured')
    • compact (Gauss points), non-compact
  • Existing literature ✅
    1. What studies have used high-order finite volume transport for atmospheric models?
    2. What high-order finite volume transport schemes exist that are suitable for arbitrary polyhedral meshes?
  • cubicFit achieves only second-order convergence ✅
  • but cubicFit uses a large non-compact stencil that should permit higher order convergence ✅
  • Advection formulation
    • order-of-accuracy analysis
  • 1D results ✅
    • 3/4-point stencils: --uuu--uu--u--|--d-->
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