[Paper Review] An implicit unified gas-kinetic wave-particle method for radiative transport process

Chang Liu, Weiming Li+2 more|arXiv (Cornell University)|Feb 13, 2023

Gas Dynamics and Kinetic Theory4 citations

TL;DR

This paper proposes an implicit unified gas-kinetic wave-particle (IUGKWP) method for radiative transport that removes the CFL time step restriction by categorizing photon transport into long- and short-mean-free-path processes. It combines implicit Monte Carlo for long-λ particles, implicit moment equations for short-λ particles, and a local integral solution of the radiative transfer equation (RTE) to achieve asymptotic-preserving and regime-adaptive behavior with second-order accuracy and reduced dissipation in optically thick regimes.

ABSTRACT

The unified gas-kinetic wave-particle method (UGKWP) has been developed for the multiscale gas, plasma, and multiphase flow transport processes for the past years. In this work, we propose an implicit unified gas-kinetic wave-particle (IUGKWP) method to remove the CFL time step constraint. Based on the local integral solution of the radiative transfer equation (RTE), the particle transport processes are categorized into the long-$λ$ streaming process and the short-$λ$ streaming process comparing to a local physical characteristic time $t_p$. In the construction of the IUGKWP method, the long-$λ$ streaming process is tracked by the implicit Monte Carlo (IMC) method; the short-$λ$ streaming process is evolved by solving the implicit moments equations; and the photon distribution is closed by a local integral solution of RTE. In the IUGKWP method, the multiscale flux of radiation energy and the multiscale closure of photon distribution are constructed based on the local integral solution. The IUGKWP method preserves the second-order asymptotic expansion of RTE in the optically thick regime and adapts its computational complexity to the flow regime. The numerical dissipation is well controlled, and the teleportation error is significantly reduced in the optically thick regime. The computational complexity of the IUGKWP method decreases exponentially as the Knudsen number approaches zero, and the computational efficiency is remarkably improved in the optically thick regime. The IUGKWP is formulated on a generalized unstructured mesh, and multidimensional 2D and 3D algorithms are developed. Numerical tests are presented to validate the capability of IUGKWP in capturing the multiscale photon transport process. The algorithm and code will apply in the engineering applications of inertial confinement fusion (ICF).

Motivation & Objective

• To overcome the severe time step restriction of explicit schemes in radiative transport simulations.
• To develop a unified, asymptotic-preserving method that adapts to all flow regimes—optically thin, transitional, and thick—without resolution constraints.
• To reduce numerical dissipation and teleportation errors in the optically thick regime while maintaining second-order accuracy.
• To enable efficient simulation of inertial confinement fusion (ICF) problems on unstructured meshes with high computational efficiency in the thick regime.
• To provide a robust, scalable algorithm for engineering applications in high-energy-density physics, particularly ICF.

Proposed method

• Introduces a physical time step $ t_p $ to distinguish long-λ (streaming-dominated) and short-λ (diffusive) photon transport processes.
• Tracks long-λ particles using an implicit Monte Carlo (IMC) method to eliminate time step restrictions.
• Evolved short-λ transport via an implicit system of moment equations derived from the radiative transfer equation (RTE).
• Closes the photon distribution using a local integral solution of the RTE, ensuring multiscale flux and closure consistency.
• Constructs a unified framework that preserves the asymptotic limit of the RTE in the optically thick regime.
• Implements the scheme on generalized unstructured meshes, enabling 2D and 3D simulations with adaptive complexity.

Experimental results

Research questions

• RQ1 Can an implicit scheme be designed to remove the CFL constraint in radiative transport while preserving asymptotic behavior?
• RQ2 How can multiscale photon transport—spanning from free-streaming to diffusive regimes—be accurately and efficiently simulated in a single framework?
• RQ3 To what extent does the IUGKWP method reduce numerical dissipation and teleportation errors in the optically thick regime compared to explicit or standard IMC methods?
• RQ4 How does the computational complexity of the IUGKWP method scale with decreasing Knudsen number, particularly in the thick regime?
• RQ5 Can the IUGKWP method achieve high accuracy and efficiency in complex 2D and 3D inertial confinement fusion (ICF) geometries?

Key findings

• The IUGKWP method achieves second-order asymptotic accuracy in the optically thick regime, correctly recovering the diffusion limit of the RTE.
• Numerical dissipation is well-controlled, and teleportation errors are significantly reduced in the optically thick regime compared to standard IMC.
• Computational complexity decreases exponentially as the Knudsen number approaches zero, leading to a dramatic efficiency gain in the thick regime.
• The method maintains stability and accuracy across all flow regimes, including optically thin, transitional, and thick, with no time step restriction.
• 2D and 3D simulations of square and circular hohlraum problems show excellent agreement with discrete ordinate (SN) results for material and radiation temperature contours and profiles.
• The 3D cylindrical hohlraum simulation successfully captures time-evolving temperature distributions and capsule surface heating over 10 ns, demonstrating robustness and scalability.