Mass Conservation and Continuity

Part 10, Chapter 10: Flow Physics, Governing Equations, and Initialization

A Balance on Every Cell

A simulator enforces conservation of mass on each grid cell: the rate of accumulation equals the net flux across the faces plus any well term, ∂∂t(ϕ ρ S)=−∇ ⁣⋅(ρ u⃗)+q\dfrac{\partial}{\partial t}(\phi,\rho,S) = -\nabla!\cdot(\rho,\vec{u}) + q.

Mass conservation and continuityinoutfulltime ->stored fluidAccumulation rate = in - out + well = 1.0 - 0.6 + 0.0 = 0.4 (filling). This continuity balance on every cell is what couples the grid.

Steady and Transient

When inflow and outflow match and no well acts, the accumulation is zero and the cell is steady. Any mismatch fills or drains the cell at a rate exactly equal to the imbalance.

What Couples the Grid

Each cell's outflow is its neighbor's inflow, so the balance written on every cell at once is what ties the whole grid into one coupled system the simulator solves together.

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