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A conservative Eulerian-Lagrangian decomposition principle for the solution of multi-scale flow problems at high Schmidt or... 1 1 Introduction 1 2 The Euler-Lagrangian decomposition method 4 2.1 Governing equations 4 2.2 Decomposition principle 5 2.3 Particle definition and translation 5 2.4 Particle distribution 8 2.5 Re-initialisation concept 9 2.6 Time stepping 10 2.7 Low-pass filtering 10 2.7.1 Gaussian filter at initialisation 11 2.7.2 Localised diffusion filter at re-initialisation 11 3 Numerical setup and test case configuration 12 3.1 Flow field setup and simulation numerics 12 3.2 Test cases 13 4 Results 13 4.1 FVM-resolved reconstruction 13 4.2 ELD-reconstruction 15 4.3 Schmidt number and ELD constant 17 4.4 Computational cost 19 5 Conclusions 22 CRediT authorship contribution statement 23 Declaration of competing interest 23 Acknowledgements 23 Appendix A An investigation on the filter width 23 Appendix B Details on the turbulent flow field 24 References 25

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nonfiction