Computing a consistent velocity vector field from a set of fluxes
AssigneeExxonMobil Upstream Research Company
InventorRossen R. Parashkevov
Life of this patent
Estimating the term…
Abstract
A method for constructing a velocity vector field from a grid and a set of fluxes for each face of the grid cells. The cells are first subdivided and internal fluxes are calculated for each cell subject to the constraints of the flux for each cell and to achieve the minimum energy state for the each cell. The minimum energy state is computed efficiently using a divergence-free correction method without introducing a pressure variable. Then, the velocity vector field is constructed from the subcell fluxes using mixed finite element interpolation.
Claims12
A computer-implemented method for constructing a velocity vector from a set of fluxes into or out of each face of a cell with a top face and a bottom face, comprising:
- divide the cell into triangular prisms with a common edge in the interior of the cell;
- create a set of equations for calculating the flux across each interior prism face;
- calculate a solution to the set of equations that minimizes the complementary energy of the cell;
- and
- using a computer to construct a velocity vector from the fluxes corresponding to the minimum complementary energy.
A computer-implemented method of calculating velocity vectors for cells in a grid from a set of fluxes across each grid boundary comprising:
- dividing a cell into subcells;
- forming an expression for the complementary energy of the cell;
- finding the minimizer of the complementary energy of the cell and calculating the internal fluxes corresponding to the minimal energy state;
- and
- using a computer to construct a velocity vector for the cell based on the internal fluxes corresponding to the minimized complementary energy.
A computer-implemented method for constructing velocity vectors from a set of fluxes between cells in a grid, comprising:
- dividing the cell into triangular subcells equal in number to the number of cell boundaries for the cell;
- estimating the flux across the boundary between any two subcells;
- calculating the flux across all other internal boundaries between subcells based on the estimated flux;
- calculating the complementary energy of the cell;
- recalculating the fluxes across every internal boundary between subcells and complementary energy to determine the set of fluxes that minimize the complementary energy of the cell;
- and
- using a computer to construct velocity vectors from the sets of fluxes that correspond to the minimum complementary energy for each cell.
A computer-implemented method for calculating a set of velocity vectors for flow across a grid of cells from a set of fluxes between each of the cells divided into triangular subcells, comprising:
- calculating a set of internal fluxes across the internal boundaries between subcells for each cell;
- calculating the complementary energy for each cell from the internal fluxes;
- adjusting calculations for internal fluxes to find a set of internal fluxes that minimizes the complementary energy;
- and
- using a computer to construct a velocity vector from the fluxes corresponding to the minimized complementary energy.
Dependencies are inferred from the claim text.