Numerical simulation of Burgers' turbulence revisited

Abstract

Abstract The stochastic solution to the Burgers' equation evolving from a random initial condition is obtained numerically by means of a conservative difference scheme. The performance of the scheme is checked by means of a number of mandatory numerical tests involving different mesh sizes. Various multi-point statistical characteristics, e.g. three-point third-order correlation and two-point third- and fourth-order correlations, are calculated from the random solution and shown graphically. The results for the correlation function and normalized spectrum are compared with earlier findings from numerical simulations of other authors performed with different numerical techniques and the agreement is quantitatively very good. A kind of stochastic self-similarity is observed for large times. In the end the usefulness of the data gathered is demonstrated through comparing the results for the statistical properties from the direct numerical simulation with the predictions of so-called ‘random-point approximation’ and the agreement turns out to be fully satisfactory.