Validation
How Meridian checks its solvers
Meridian compares its solvers with NAFEMS benchmarks and with analytic solutions.
- Each case runs on a series of meshes.
- For each case, Meridian calculates the observed order of convergence, a Richardson extrapolation and the grid convergence index (GCI). The method follows ASME V&V 20-2009 and Celik (2008).
- The test suite makes the verification manual. A test fails when a value goes out of its tolerance.
Structural and thermal benchmarks
All of these cases pass.
| Group | Cases |
|---|---|
| Linear statics | LE1, LE2, LE3, LE5, LE6, LE7, LE8, LE10, LE11 |
| Free vibration | FV12, FV15, FV16, FV22, FV32, FV42, FV52 |
| Thermal | T3, T4 |
| Plasticity | NL-S1, NL2 |
| Contact | NL-C1 (Hertz line contact) |
Shell elements
- A simply supported plate deflects within 0.10 % of the Timoshenko value.
- A 200 x 200 x 5 mm plate needs about 1,060 shell nodes. The same plate needs about 552,000 nodes with solid elements.
Flow benchmarks
| Case | Result |
|---|---|
| F1, square duct | f·Re error +0.37 % |
| F2, Schaefer-Turek cylinder | Cd error +1.2 % |
Sphere drag
| Reynolds number | Drag error |
|---|---|
| 100 | +1.2 % |
| 300 | -2.4 % |
| 1,000 | -2.0 % |
| 3,000 | +9.5 % |
| 10,000 | +15.8 % |
High Reynolds number cases
| Case | Result |
|---|---|
| NACA 0012 airfoil at Re 1,000,000 | Cd is 3.1 times too high. Cl is -6.7 % at 4° and -7.6 % at 8°. |
| Ahmed body at Re 1,000,000, slant 25° and 35° | Cd is +27 % (25°) and +38 % (35°) more than the published data (measured at Re 4,300,000). |
These results show why the flow solver is Beta above Re of about 1,000.
Internal flow
These laminar cases are validated:
- Hagen-Poiseuille pipe flow.
- Pipe entrance length.
- Lid-driven cavity at Re 100 and Re 1,000.
- Backward-facing step at Re 800.
- Sudden expansion.
Turbulent internal flow is not validated.
Known limits
Solid elements
- A support on a line (an edge) is singular. The results near it do not converge to a fixed value.
Shell elements
- Use solid elements when the wall thickness is more than about 0.1 of the span or of the radius.
- Buckling load factors are linear values. They do not include imperfections. Imperfections can lower the real collapse load.
- With shell elements, these are not available: transient thermal, nonlinear, fatigue, flow, contacts and connectors.
Flow
- Above Re of about 1,000, external drag is 2 to 3 times too high, and lift changes with the grid.
- If the mean y+ is more than about 300, the drag is too high.
- Compare lift only between runs with the same refinement levels and the same refinement box.
- Put at least 32 cells across a sphere diameter and at least 128 cells along a chord.
For the use of these solvers, refer to Structural simulation and Fluid simulation.