Field and simulation examples
These examples compute magnetic, electric and thermal fields, flow, elasticity and diffusion on geometry drawn in planex2d. planex2d draws the part, names the edges and regions that carry the boundary conditions, and glues several materials into one geometry. In most examples, netgen meshes it and NGSolve solves the field, and the solution is compared with a closed form, an empirical law or a published value, such as Hammerstad and Jensen’s microstrip formulas, Peterson’s stress concentration
factors or the cutoff of a WR-90 waveguide.
In this section
Surface magnet motor A lamination glued into regions, its field, and a 12-slot design under load. Heat sink Conduction and convection in an extruded profile, one fin against fin theory. Hilbert heater A heater track along a Hilbert curve, with current, Joule heat and temperature. Parallelogram flexure A flexure stage from one block, pushed sideways in a 3D elasticity solve. Vivaldi antenna An exponential tapered slot with a round cavity and a radial stub. Voronoi bone Some 6000 struts united at once, pressed against a scaling law. Runs in the browser Lens ray tracing A biconvex lens as two intersected discs, with Snell's law and chief and marginal rays. Airplane windows Round, oval and square windows in a pressurized skin, against Kirsch, Inglis and Williams. The Tesla valve A valve without moving parts: no effect in Stokes flow, 1.6 times the pressure one way at Re 200. The Venturi meter Bernoulli's equation along the centerline of a Navier-Stokes flow, and the meter's discharge coefficient. The hydraulic diameter Laminar flow through five duct sections against the exact solutions, and how far each is from a pipe. The Joukowski airfoil Potential flow with the Kutta condition, the circulation and the lift against the exact values. Microstrip impedance A trace on FR-4 from two electrostatic solves, against Hammerstad and Jensen, and its width for 50 Ω. The Faraday cage A ring of thin wires in the field of a line charge: shielding in proportion to the number of wires, not exponential. Sharp or blunt lightning rods The field at the tip grows as E0 (1 + a/b), but above it a blunt rod overtakes a sharp one. The skin effect Alternating current in a copper wire against the Bessel solution, and a flat bar where it gathers at the edges. Waveguide cutoff The modes of a WR-90 and a round guide against the closed forms, and a ridge that lowers the cutoff. A photonic crystal The TM bands of a lattice of rods from Bloch modes, and its band gap against the textbook's 31.4 %. Stress at a shoulder fillet A stepped bar as a parametric sketch, its stress concentration factor against the body force method and Peterson's chart. Open and closed sections in torsion A tube and the same tube slit: over a thousand times the stiffness, against Bredt and s t³/3. The Halbach array Magnets whose field is on one side only, as a periodic cell, against Mallinson's and Halbach's formulas. Turing patterns Spots growing out of noise at the rates the linear analysis predicts, and a tapering tail that ends in rings. The Helmholtz coil Two coils one radius apart: the field in their middle, uniform to the fourth order, against the loop formula. Runs in the browser Random walks and electric networks The chance that a random walker leaves a hall by the front door is a voltage: a resistor network on the grid against 4000 walkers. Designing an auxetic material A periodic cell shaped by a level-set method until the lattice gets wider when pulled, then traced as a clean cell. See Examples
