Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

Yang, Yunan; Silantyev, Denis; Caflisch, Russel

doi:10.1016/j.jcp.2023.112247

Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

Journal Article · Tue May 30 00:00:00 EDT 2023 · Journal of Computational Physics

DOI:https://doi.org/10.1016/j.jcp.2023.112247· OSTI ID:2419320

^[1]; Silantyev, Denis ^[2]; Caflisch, Russel ^[3]

Eidgenoessische Technische Hochschule (ETH), Zurich (Switzerland); OSTI
University of Colorado, Colorado Springs, CO (United States)
New York University (NYU), NY (United States)

We derive an adjoint method for the Direct Simulation Monte Carlo (DSMC) method for the spatially homogeneous Boltzmann equation with a general collision law. This generalizes our previous results in Caflisch et al., which was restricted to the case of Maxwell molecules, for which the collision rate is constant. The main difficulty in generalizing the previous results is that a rejection sampling step is required in the DSMC algorithm in order to handle the variable collision rate. We find a new term corresponding to the so-called score function in the adjoint equation and a new adjoint Jacobian matrix capturing the dependence of the collision parameter on the velocities. The new formula works for a much more general class of collision models.

View Accepted Manuscript (DOE)

Research Organization:: New York University (NYU), NY (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF)

Grant/Contract Number:: FG02-86ER53223

OSTI ID:: 2419320

Journal Information:: Journal of Computational Physics, Journal Name: Journal of Computational Physics Journal Issue: C Vol. 488; ISSN 0021-9991

Publisher:: ElsevierCopyright Statement

Country of Publication:: United States

Language:: English

References (16)

On a simulation scheme for the Boltzmann equation Babovsky, H.; Neunzert, H. Mathematical Methods in the Applied Sciences, Vol. 8, Issue 1 https://doi.org/10.1002/mma.1670080114	journal	January 1986
An energy-transport model for semiconductors derived from the Boltzmann equation Ben Abdallah, N.; Degond, P.; Genieys, S. Journal of Statistical Physics, Vol. 84, Issue 1-2 https://doi.org/10.1007/BF02179583	journal	July 1996
On a Kinetic Model for a Simple Market Economy Cordier, Stephane; Pareschi, Lorenzo; Toscani, Giuseppe Journal of Statistical Physics, Vol. 120, Issue 1-2 https://doi.org/10.1007/s10955-005-5456-0	journal	July 2005
A Review of Mathematical Topics in Collisional Kinetic Theory Villani, Cédric Handbook of Mathematical Fluid Dynamics https://doi.org/10.1016/S1874-5792(02)80004-0	book	January 2002
Particle simulation of Coulomb collisions: Comparing the methods of Takizuka & Abe and Nanbu Wang, Chiaming; Lin, Tungyou; Caflisch, Russel Journal of Computational Physics, Vol. 227, Issue 9 https://doi.org/10.1016/j.jcp.2007.12.027	journal	April 2008
Adjoint DSMC for nonlinear Boltzmann equation constrained optimization Caflisch, Russel; Silantyev, Denis; Yang, Yunan Journal of Computational Physics, Vol. 439 https://doi.org/10.1016/j.jcp.2021.110404	journal	August 2021
Topology optimization for rarefied gas flow problems using density method and adjoint IP-DSMC Guan, Kaiwen; Matsushima, Kei; Noguchi, Yuki Journal of Computational Physics, Vol. 474 https://doi.org/10.1016/j.jcp.2022.111788	journal	February 2023
Collective learning modeling based on the kinetic theory of active particles Burini, D.; De Lillo, S.; Gibelli, L. Physics of Life Reviews, Vol. 16 https://doi.org/10.1016/j.plrev.2015.10.008	journal	March 2016
Direct Simulation and the Boltzmann Equation Bird, G. A. Physics of Fluids, Vol. 13, Issue 11 https://doi.org/10.1063/1.1692849	journal	January 1970
Variable soft sphere molecular model for inverse‐power‐law or Lennard‐Jones potential Koura, Katsuhisa; Matsumoto, Hiroaki Physics of Fluids A: Fluid Dynamics, Vol. 3, Issue 10 https://doi.org/10.1063/1.858184	journal	October 1991
Derivation of the Boltzmann Equation for Financial Brownian Motion: Direct Observation of the Collective Motion of High-Frequency Traders Kanazawa, Kiyoshi; Sueshige, Takumi; Takayasu, Hideki Physical Review Letters, Vol. 120, Issue 13 https://doi.org/10.1103/PhysRevLett.120.138301	journal	March 2018
A Convergence Proof for Nanbu’s Simulation Method for the Full Boltzmann Equation Babovsky, Hans; Illner, Reinhard SIAM Journal on Numerical Analysis, Vol. 26, Issue 1 https://doi.org/10.1137/0726004	journal	February 1989
A Fast Spectral Method for the Boltzmann Collision Operator with General Collision Kernels Gamba, Irene M.; Haack, Jeffrey R.; Hauck, Cory D. SIAM Journal on Scientific Computing, Vol. 39, Issue 4 https://doi.org/10.1137/16M1096001	journal	January 2017
Vehicular traffic, crowds, and swarms: From kinetic theory and multiscale methods to applications and research perspectives Albi, G.; Bellomo, N.; Fermo, L. Mathematical Models and Methods in Applied Sciences, Vol. 29, Issue 10 https://doi.org/10.1142/S0218202519500374	journal	September 2019
Direct Simulation Scheme Derived from the Boltzmann Equation. I. Monocomponent Gases Nanbu, Kenichi Journal of the Physical Society of Japan, Vol. 49, Issue 5 https://doi.org/10.1143/JPSJ.49.2042	journal	November 1980
Kinetic description of optimal control problems and applications to opinion consensus Albi, Giacomo; Herty, Michael; Pareschi, Lorenzo Communications in Mathematical Sciences, Vol. 13, Issue 6 https://doi.org/10.4310/CMS.2015.v13.n6.a3	journal	January 2015

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Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
Adjoint-state method
Boltzmann equation
DSMC
Direct simulation Monte Carlo methods
Optimization

Adjoint DSMC for nonlinear spatially-homogeneous Boltzmann equation with a general collision model

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