Choosing solver fidelity

Fast sections, radial sampling and full 3-D—plus their limits.

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Four tiers, one machine Sections are measured against 3-D Use 3-D to confirm Keep model boundaries visible

Conceptual diagram · not to scale · not a computed field or mesh. Scroll the diagram sideways to read all labels. Magnet recoil permeability and effective gap set this estimate; iron reluctance and leakage are omitted.

Milliseconds · illustrative workload

Find a starting point.

A simplified magnet-and-gap circuit estimates airgap flux density for rapid design screening.

Use it for: Sizing and broad parameter screens
Keep in mind: No resolved local field, cogging or end effects

01Four tiers, one machine

The same machine description runs at four fidelities. Each answers a different question:

Analytic: a magnetic circuit, in milliseconds. Use it for sizing and for grids of thousands of designs. Trust the direction, not the number.
2-D: one section unrolled at the mean radius, in about a second per rotor angle. Use it to rank designs that differ in one parameter.
Quasi-3-D: several radial sections, solved in parallel and summed. Use it for design iteration, flux maps, skew and the coupled thermal loop.
3-D: a periodic sector or the whole machine, in tens of seconds to minutes per angle. Use it to confirm a final design and for inductances, cogging, magnet-corner fields and end effects.

A quantity a tier cannot resolve, such as ripple on a section, comes back marked as not resolved, never as zero. It cannot win a sweep by accident.

02Sections are measured against 3-D

The sections' mean-torque bias against 3-D is measured per architecture, not assumed: within about 2 % on 2-D and up to about 5 % on quasi-3-D. A result offers its own architecture's correction; it is never applied silently.

Sections cannot see leakage outside the section, so they read Ld and Lq about 15–19 % low. They also miss magnet overhang and radial end effects. No correction is applied for these.

03Use 3-D to confirm

The native 3-D solver runs on a structured grid graded toward the iron. The grid's remaining error in torque is about 0.1–0.4 % on the reference machines. A two-grid error estimate and an optional second formulation can bound it on your own machine.

Refine the grid and angular sampling deliberately, and compare like quantities. A low residual alone does not prove that cogging, leakage or a local peak field is resolved. On a 2-D section a demagnetisation fail is a fail, but a pass is not a pass.

04Keep model boundaries visible

Flux maps store mean d-q surfaces. They hold no rotor-angle harmonics, so a system model built on them has no ripple.
Eddy currents are solved in the magnets on native 3-D, and in solid rotor discs and magnets by time-harmonic solves. Elsewhere eddy and AC losses are bounded estimates from the magnetostatic field.
Time-domain analysis (voltage-fed circuits, inverter switching, transients) is in development and not yet in the app. Inverter device losses are outside the model.
Thermal networks and the 3-D conduction model are not a general CFD or conjugate heat-transfer workflow.