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ABSTRACT
A newly developed efficient and fully implicit method for multiblock mesh coupling that preserves the convergence characteristics of single-block meshing is presented. The technique is developed in the context of an unstructured pressure-based collocated finite-volume method, is applicable to both segregated and coupled flow solvers, and is ideal for code parallelization. The discretization at interfaces is performed in a separate step to stitch the regions sub-matrices into a global matrix. By solving the global matrix, the solution achieved to the multiregion problem is exactly the one that would result from a single-mesh discretization. The method is tested by solving three laminar flow problems. Solutions are obtained by meshing the domain as one block or by subdividing it into a number of blocks with non-matching grids at interfaces. Results show the very tight coupling at interfaces with a convergence rate that is independent of the number of blocks used.
Nomenclature
| = | coefficients in the discretized equations | |
| = | source term in the discretized ϕ equation | |
| B | = | source term in the momentum equation |
| C | = | main grid point |
| dCF | = | vector joining the grid points C and F |
| dCF | = | magnitude of dCF |
| D | = | operator used in the pressure equation |
| = | components of the D operator | |
| E | = | component of the surface vector in the direction of dCF |
| E | = | magnitude of E |
| F | = | refers to neighbor of the C grid point |
| g | = | geometric interpolation factor |
| I | = | identity matrix |
| = | convection flux | |
| = | diffusion flux | |
| = | mass flow rate at control volume face f | |
| p | = | pressure |
| S | = | surface vector |
| = | Components of the surface vector Sat element face f | |
| u, v | = | velocity components in x- and y-direction, respectively |
| v | = | velocity vector |
| V | = | volume of element |
| Greek symbols | = | |
| ϕ | = | scalar variable |
| μ | = | dynamic viscosity |
| Γ | = | diffusion coefficient |
| ρ | = | fluid density |
| τ | = | deviatoric stress tensor |
| ∂V | = | surface area of cell volume V |
| Subscripts | = | |
| C | = | main grid point |
| f | = | control volume face |
| F | = | F grid point |
| nb | = | values at the faces obtained by interpolation between C and its neighbors |
| NB | = | neighbors of the C grid point |
| Superscripts | = | |
| p | = | pressure |
| u | = | u-velocity component |
| v | = | v-velocity component |
| ′ | = | correction |
| * | = | value at the previous iteration |
| = | interpolated value |
Nomenclature
| = | coefficients in the discretized equations | |
| = | source term in the discretized ϕ equation | |
| B | = | source term in the momentum equation |
| C | = | main grid point |
| dCF | = | vector joining the grid points C and F |
| dCF | = | magnitude of dCF |
| D | = | operator used in the pressure equation |
| = | components of the D operator | |
| E | = | component of the surface vector in the direction of dCF |
| E | = | magnitude of E |
| F | = | refers to neighbor of the C grid point |
| g | = | geometric interpolation factor |
| I | = | identity matrix |
| = | convection flux | |
| = | diffusion flux | |
| = | mass flow rate at control volume face f | |
| p | = | pressure |
| S | = | surface vector |
| = | Components of the surface vector Sat element face f | |
| u, v | = | velocity components in x- and y-direction, respectively |
| v | = | velocity vector |
| V | = | volume of element |
| Greek symbols | = | |
| ϕ | = | scalar variable |
| μ | = | dynamic viscosity |
| Γ | = | diffusion coefficient |
| ρ | = | fluid density |
| τ | = | deviatoric stress tensor |
| ∂V | = | surface area of cell volume V |
| Subscripts | = | |
| C | = | main grid point |
| f | = | control volume face |
| F | = | F grid point |
| nb | = | values at the faces obtained by interpolation between C and its neighbors |
| NB | = | neighbors of the C grid point |
| Superscripts | = | |
| p | = | pressure |
| u | = | u-velocity component |
| v | = | v-velocity component |
| ′ | = | correction |
| * | = | value at the previous iteration |
| = | interpolated value |