Adaptive mesh refinement applied to the scalar transported PDF equation in a turbulent jet

Abstract

SUMMARYThis paper describes a novel solution method for the transported probability density function (PDF) equation for scalars (compositions). In contrast to conventional solution methods based on the Monte Carlo approach, we use a finite-volume method combined with adaptive mesh refinement (AMR) applied in both physical and compositional space. The obvious advantage of this over a uniform grid is that fine meshes are only used where the solution requires high resolution. The efficiency of the method is demonstrated by a number of tests involving a turbulent jet flow with up to two scalars (both reacting and non-reacting). We find that the AMR calculation can be at a fraction of the computer cost of a uniform grid calculation with the same accuracy.

Prediction of external intermittency using RANS-based turbulence modelling and a transported PDF approach

“…It can be seen that the effect of the intermittency is not only responsible for improved predictions on the jet centreline, but also for the bimodal distributions associated with its increasing influence with radial distance. Apart from on the centre-line, the implementation of  in the LMSE molecular mixing model, as seen in Equation (8), is the primary influence in this respect, with the effect of  in the flow Equations (11) and (13) a secondary effect. All the present results given in Figure 6 are also superior to those obtained in earlier work [15] which used the three-part, prescribed PDF approach of Effelsberg and Peters [27] and which failed to predict the bimodal distributions observed experimentally.…”

“…This contrasts with more conventional approaches which are based on the use of finitevolume methods in physical space, and Monte Carlo methods in compositional space for solution of the PDF equation. This work [7,8] also demonstrated that, for small numbers of scalar variables, AMR provides improved accuracy, run times and ease of use over alternative Monte Carlo approaches. AMR is now a well-established technique, having its earliest applications in two-dimensional shock problems [9,10], with subsequent extension to three-dimensional flows [11] and implementation on parallel computers [12].…”

“…So, for example, the maximum number of grid levels will be used in composition space if P is close to a delta-function, whereas a smaller number of levels will be used if it is smooth. Further details are given in [7,8].…”

“…Earlier work by the authors [7,8] has demonstrated the application of an AMR finite-volume technique in both physical and compositional space, with the latter permitting solution of the transported PDF equation. This contrasts with more conventional approaches which are based on the use of finitevolume methods in physical space, and Monte Carlo methods in compositional space for solution of the PDF equation.…”

Application of the PDF transport model to nonreacting jets using an adaptive Monte Carlo method

“…For PDF transport modeling, there has been little investigation of techniques to reduce the runtime for the solution of the PDF transport model. The exception to this is the work of Fairweather et al [17][18][19], where an adaptive finite volume mesh algorithm is used to solve the PDF transport model for some idealized nonreacting and reacting flows. This is computationally frugal for many situations, where only a small region of parameter space requires a fine grid to resolve the PDF and is a technique that has been applied successfully to shock capturing in compressible flows [20] and radiation heat flux calculation in fire modeling [21].…”