NeuralFlowTheory & User Reference Manual
Solution Monitoring and Integral Reports
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Solution Monitoring and Integral Reports

NeuralFlow provides surface integrals, flux balances, force/moment coefficients and point probes so users can judge both convergence and engineering performance. These quantities are not merely display features: they are the recommended way to verify conservation and to decide whether a residual-converged solution is also stable in the quantity of interest.

Surface fields and averages

For a surface , the area-weighted mean of a scalar is

When a mass-weighted report is requested, the weighting is based on signed or directed carrier mass flow as appropriate to the report definition,

Surface fields include density, pressure, temperature, total pressure, total temperature, velocity, Mach number, vorticity magnitude, enthalpy/energy and turbulence quantities.

Flux reports

Carrier mass flow through a surface is

The dilute dispersed-phase counterpart is

Total wall/surface heat rate follows

In axisymmetric calculations the surface-integration path applies the corresponding rotational geometric weighting.

Forces, moments and coefficients

The pressure and viscous forces are

Moment about reference point is

With dynamic pressure ,

The reported center of pressure is derived from the force/moment balance relative to the selected reference geometry.

Point probes and convergence monitoring

Point probes and iterative monitors provide local solution histories, residual evolution, time-step/CFL information and solver status. These diagnostics do not alter the governing residual; they sample or reduce the distributed solution state.