finiteVolumen

finiteVolumen, often referred to as the finite volume method (FVM), is a numerical discretization technique for solving partial differential equations, particularly conservation laws. It is widely used in computational fluid dynamics to simulate flows, heat transfer, and related transport phenomena. The method emphasizes local conservation of quantities such as mass, momentum, and energy.

Conceptually, the domain is divided into a set of non-overlapping control volumes (cells). The governing equations are integrated over each cell, converting differential equations into algebraic statements about the time rate of change of cell-averaged values and the fluxes across cell faces. The resulting scheme enforces conservation at the discrete level.

Fluxes across faces are approximated using information from neighboring cells, often via Riemann solvers or upwind reconstructions. For higher order accuracy, slope limiter reconstructions (e.g., MUSCL) or higher-order methods (PPM, WENO) are used. Time integration can be explicit (e.g., Runge-Kutta) or implicit, with stability governed by the Courant–Friedrichs–Lewy (CFL) condition for explicit schemes.

Mesh flexibility is a key strength: finiteVolumen works on structured and unstructured grids, including triangles and tetrahedra, enabling complex geometries. Unknowns may be stored at cell centers (cell-centered FV) or at cell faces (staggered FV).

Applications include simulating compressible and incompressible flows, heat and mass transfer, porous media, and reactive transport. Advantages include local conservation, robustness for shocks, and geometric flexibility; limitations include numerical diffusion and challenges achieving very high-order accuracy. Related methods are the finite difference method and finite element method; many CFD codes combine FV with specialized solvers such as SIMPLE or PISO for incompressible flow.