Simulation chops the world into small boxes

Discretisation, and what is lost when a continuum becomes cells.

Before a solver can do any arithmetic at all, the smooth, continuous shape of a real part has to be cut into a large number of small, flat-sided pieces, and that cutting step throws away information the moment it happens, whether or not anybody notices.

A curve becomes a list of flat facets

A real component, a pipe bend or a cast bracket, has surfaces that curve smoothly. A solver's arithmetic needs a finite list of regions instead, each with a single value for temperature or pressure or stress, connected to a known set of neighbours. So the geometry is first cut into that list, a process called discretisation, and every curved surface in the original becomes, at the scale of one piece, a small flat facet standing in for the curve.

Each piece is called a cell, and a mesh for even a modest component runs into the hundreds of thousands of them. The curve, as a curve, exists only in the original drawing, and once the geometry has been cut the solver never sees it again, so no arithmetic performed afterwards can recover detail that was smoothed away during the cut.

The cardboard hillside

Anyone who has built a model hillside from a stack of cardboard layers, each cut to a different contour line and glued on top of the last, knows what this costs. From a few paces back it reads as a smooth slope, but a fingertip finds a staircase. Cutting more, thinner layers spreads the same total rise over more, smaller jumps until a hand can no longer feel them, though the model only ever becomes a better staircase.

A meshed part is that hillside built from cells, and refinement shrinks its steps quickly. Cut a circle into ten straight facets and the flat edges sag inside the true curve by about 5 percent of its radius at their midpoints; cut it into a hundred and the sag falls to about 0.05 percent, so ten times as many facets gives a gap a hundred times smaller, though never zero, since a mesh is a finite list and a curve is not.

Two meshes, two answers

The geometry fed into a solver is therefore never quite the geometry on the drawing, and the difference is largest where curvature is tightest: fillets, blend radii, anywhere a surface turns sharply in a small space. A designer who assumes the simulation is working on the real part will be surprised when a result shifts after nothing but the mesh was refined around one of those curves.

Two people meshing the same drawing can likewise produce two different answers before either has touched a physics setting, because every choice about how finely to cut a curve decides how much of the real geometry survives into the study. Clicking through that step as a formality is the most common way a simulation ends up describing a part slightly different from the one that will be built.