Numerical verification of an Industrial code to simulate accurately large scale Hydrodynamics events

Abstract

The use of finite-precision arithmetic generates round-off errors at each arithmetical expression so some mathematical properties are lost during the computing of a numerical code. Consequently, the same numerical code using the same input data could produce different results on different computers. The round-off error propagation is exacerbated in High Performance Computing since trillions of floating arithmetic operations can be performed each second. Moreover, due to the domain decomposition, the floating point arithmetic operations are not performed in the same order. There is therefore a need to detect the effect of round-off error propagation in order to make confidence about the results of the simulation. This paper deals with an overview of the numerical verification activities performed at EDF R&D on the parallel TELEMAC-2D code modelling the 2D free surface hydrodynamics. Firstly, a framework developed at EDF R&D to study the effect of the round-off error propagation on the quality of a simulation is exposed. Then, the xD+P approach which has been proposed to measure the numerical quality of the computed values is presented. Finally, a recent work dealing with the improvement of the floating point summation is discussed.