Theoretical analysis for achieving high-order spatial accuracy in Lagrangian/Eulerian source terms
In a fully coupled Lagrangian/Eulerian two-phase calculation, the source terms from computational particles must be agglomerated to nearby gas-phase nodes. Existing methods are capable of accomplishing this particle-to-gas coupling with second-order accuracy. However, higher-order methods would be useful for applications such as two-phase direct numerical simulation and large eddy simulation. A theoretical basis is provided for producing high spatial accuracy in particle-to-gas source terms with low computational cost. The present work derives fourth- and sixth-order accurate methods, and the procedure for even higher accuracy is discussed. The theory is also expanded to include two- and three-dimensional calculations. One- and two-dimensional tests are used to demonstrate the convergence of this method and to highlight problems with statistical noise. Finally, the potential for application in computational fluid dynamics codes is discussed. It is concluded that high-order kernels have practical benefits only under limited ranges of statistical and spatial resolution. Additionally, convergence demonstrations with full CFD codes will be extremely difficult due to the worsening of statistical errors with increasing mesh resolution. Copyright (c) 2006 John Wiley & Sons, Ltd.
two-phase and multiphase flows numerical methods stochastic particle methods particle methods and lattice-gas methods