A Stochastic Weighted Particle Method for Coagulation-Advection Problems

A spatially resolved stochastic weighted particle method for inception--coagulation--advection problems is presented. Convergence to a deterministic limit is briefly studied. Numerical experiments are carried out for two problems with very different coagulation kernels. These tests show the method to be robust and confirm the convergence properties. The robustness of the weighted particle method is shown to contrast with two direct simulation algorithms which develop instabilities.

[1]  A Sectional Model for Investigating Microcontamination in a Rotating Disk CVD Reactor , 2004 .

[2]  Graeme A. Bird,et al.  Molecular Gas Dynamics , 1976 .

[3]  Y. Efendieva,et al.  Hierarchical hybrid Monte-Carlo method for simulation of two-component aerosol nucleation, coagulation and phase segregation , 2002 .

[4]  Flavius Guiaş.  A stochastic approach for simulating spatially inhomogeneous coagulation dynamics in the gelation regime , 2009 .

[5]  Markus Kraft,et al.  SURFACE CHEMISTRY AND PARTICLE SHAPE: PROCESSES FOR THE EVOLUTION OF AEROSOLS IN TITAN's ATMOSPHERE , 2011 .

[6]  Flavius Guias.  CONVERGENCE PROPERTIES OF A STOCHASTIC MODEL FOR COAGULATION-FRAGMENTATION PROCESSES WITH DIFFUSION , 2001 .

[7]  Andreas Eibeck,et al.  Stochastic Particle Approximations for Smoluchoski’s Coagualtion Equation , 2001 .

[8]  Yasushi Fujiyoshi,et al.  Monte Carlo Simulation of the Formation of Snowflakes , 2005 .

[9]  Themis Matsoukas,et al.  Bicomponent aggregation in finite systems , 2010 .

[10]  W. Wagner.  A convergence proof for Bird's direct simulation Monte Carlo method for the Boltzmann equation , 1992 .

[11]  Takuji Nishimura,et al.  Mersenne twister: a 623-dimensionally equidistributed uniform pseudo-random number generator , 1998, TOMC.

[12]  Michail A. Gallis,et al.  Accuracy and efficiency of the sophisticated direct simulation Monte Carlo algorithm for simulating noncontinuum gas flows , 2009 .

[13]  Markus Kraft,et al.  Developing the PAH-PP soot particle model using process informatics and uncertainty propagation , 2011 .

[14]  Robert I. A. Patterson,et al.  Stochastic weighted particle methods for population balance equations with coagulation, fragmentation and spatial inhomogeneity , 2015, J. Comput. Phys..

[15]  Wolfgang Wagner,et al.  Convergence of the Stochastic Weighted Particle Method for the Boltzmann Equation , 2003, SIAM J. Sci. Comput..

[16]  M. Kraft,et al.  A stochastic approach to calculate the particle size distribution function of soot particles in laminar premixed flames , 2003 .

[17]  R. Rudnicki,et al.  Phytoplankton Dynamics: from the Behavior of Cells to a Transport Equation , 2006 .

[18]  M. Thomson,et al.  Modeling of soot aggregate formation and size distribution in a laminar ethylene/air coflow diffusion flame with detailed PAH chemistry and an advanced sectional aerosol dynamics model , 2009 .

[19]  Andreas Eibeck,et al.  Stochastic interacting particle systems and nonlinear kinetic equations , 2003 .

[20]  Graeme A. Bird,et al.  Approach to Translational Equilibrium in a Rigid Sphere Gas , 1963 .

[21]  Alejandro L. Garcia,et al.  A Monte Carlo simulation of coagulation , 1987 .

[22]  Henning Bockhorn,et al.  Calculation of the size distribution function of soot particles in turbulent diffusion flames , 2007 .

[23]  Robert I. A. Patterson,et al.  A predictor-corrector algorithm for the coupling of stiff ODEs to a particle population balance , 2009, J. Comput. Phys..

[24]  Madalina Deaconu,et al.  A pure jump Markov process associated with Smoluchowski's coagulation equation , 2002 .

[25]  D. Marchisio.  On the use of bi-variate population balance equations for modelling barium titanate nanoparticle precipitation , 2009 .

[26]  Kang Y. Huh,et al.  Prediction of soot particle size distribution for turbulent reacting flow in a diesel engine , 2011 .

[27]  R. I. A. PATTERSON,et al.  The Linear Process Deferment Algorithm: A new technique for solving population balance equations , 2006, SIAM J. Sci. Comput..

[28]  Axel Klar,et al.  A particle-particle hybrid method for kinetic and continuum equations , 2009, J. Comput. Phys..

[29]  Volker John,et al.  A numerical method for the simulation of an aggregation‐driven population balance system , 2012 .