Conservation properties of unstructured staggered mesh schemes
Journal Article
·
· Journal of Computational Physics
Classic Cartesian staggered mesh schemes have a number of attractive properties. They do not display spurious pressure modes and they have been shown to locally conserve, mass, momentum, kinetic energy, and circulation to machine precision. Recently, a number of generalizations of the staggered mesh approach have been proposed for unstructured (triangular or tetrahedral) meshes. These unstructured staggered mesh methods have been created to retain the attractive pressure aspects and mass conservation properties of the classic Cartesian mesh method. This work addresses the momentum, kinetic energy, and circulation conservation properties of unstructured staggered mesh methods. It is shown that with certain choices of the velocity interpolation, unstructured staggered mesh discretization of the divergence form of the Navier-Stokes equations can conserve kinetic energy and momentum both locally and globally. In addition, it is shown that unstructured staggered mesh discretization of the rotational form of the Navier-Stokes equations can conserve kinetic energy and circulation both locally and globally. The analysis includes viscous terms and a generalization of the concept of conservation in the presence of viscosity to include a negative definite dissipation term in the kinetic energy equation. These novel conserving unstructured staggered mesh schemes have not been previously analyzed. It is shown that they are first-order accurate on nonuniform two-dimensional unstructured meshes and second-order accurate on uniform unstructured meshes. Numerical confirmation of the conservation properties and the order of accuracy of these unstructured staggered mesh methods is presented.
- Research Organization:
- Univ. of Massachusetts, Amherst, MA (US)
- Sponsoring Organization:
- US Department of Energy
- OSTI ID:
- 20020799
- Journal Information:
- Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: 1 Vol. 159; ISSN JCTPAH; ISSN 0021-9991
- Country of Publication:
- United States
- Language:
- English
Similar Records
Multidimensional discretization of conservation laws for unstructured polyhedral grids
Differencing the diffusion equation on unstructured meshes in 2-D
Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations
Conference
·
Mon Aug 22 00:00:00 EDT 1994
·
OSTI ID:35336
Differencing the diffusion equation on unstructured meshes in 2-D
Technical Report
·
Mon Oct 24 00:00:00 EDT 1994
·
OSTI ID:46726
Functional entropy variables: A new methodology for deriving thermodynamically consistent algorithms for complex fluids, with particular reference to the isothermal Navier–Stokes–Korteweg equations
Journal Article
·
Sun Sep 01 00:00:00 EDT 2013
· Journal of Computational Physics
·
OSTI ID:22230783