A Picard Newton method to solve non linear airflow networks

TL;DR

This paper introduces a Picard Newton method to improve the initialization of pressure calculations in nonlinear airflow networks within building simulations, enhancing convergence in complex models especially for open buildings in tropical climates.

Contribution

The paper proposes using the Picard method to initialize zone pressures in nonlinear airflow network solving, improving convergence of the Newton-Raphson method in building simulation software.

Findings

Picard method effectively initializes zone pressures.

Improved convergence speed of Newton-Raphson method.

Validated with real test case experiment.

Abstract

In detailled buiding simulation models, airflow modelling and solving are still open and crucial problems, specially in the case of open buildings as encountered in tropical climates. As a consequence, wind speed conditioning indoor thermal comfort or energy needs in case of air conditionning are uneasy to predict. A first part of the problem is the lack of reliable and usable large opening elementary modelling and another one concerns the numerical solving of airflow network. This non linear pressure system is solved by numerous methods mainly based on Newton Raphson (NR) method. This paper is adressing this part of the difficulty, in our software CODYRUN. After model checks, we propose to use Picard method (known also as fixed point) to initialise zone pressures. A linear system (extracted from the non linear set of equations) is solved around 10 times at each time step and NR uses this result for initial values. Known to be uniformly but slowly convergent, this method appears to be really powerful for the building pressure system. The comparison of the methods in terms of number of iterations is illustrated using a real test case experiment.