3-Dimensional Hybrid Continuum-Atomistic Simulations for Multiscale Hydrodynamics

Abstract

We present an adaptive mesh and algorithmic refinement (AMAR) scheme for modeling multi-scale hydrodynamics. The AMAR approach extends standard conservative adaptive mesh refinement (AMR) algorithms by providing a robust flux-based method for coupling an atomistic fluid representation to a continuum model. The atomistic model is applied locally in regions where the continuum description is invalid or inaccurate, such as near strong flow gradients and at fluid interfaces, or when the continuum grid is refined to the molecular scale. The need for such “hybrid” methods arises from the fact that hydrodynamics modeled by continuum representations are often under-resolved or inaccurate while solutions generated using molecular resolution globally are not feasible. In the implementation described herein, Direct Simulation Monte Carlo (DSMC) provides an atomistic description of the flow and the compressible two-fluid Euler equations serve as our continuum-scale model. The AMR methodology provides local grid refinement while the algorithm refinement feature allows the transition to DSMC where needed. The continuum and atomistic representations are coupled by matching fluxes at the continuum-atomistic interfaces and by proper averaging and interpolation of data between scales. Our AMAR application code is implemented in C++ and is built upon the SAMRAI (Structured Adaptive Mesh Refinement Application Infrastructure) framework developed at Lawrence Livermore National Laboratory. SAMRAI provides the parallel adaptive gridding algorithm and enables the coupling between the continuum and atomistic methods.

Hybrid simulations of rarefied supersonic gas flows in micro-nozzles

“…A discussion on the major considerations involved with hybrid models and a summary of the state-of-art is provided by Wu and coworkers and by Wijesinghe and Hadjiconstantinou in [20,21]. Different hybrid models have been proposed to couple DSMC and Stokes equations [22], DSMC and incompressible Navier-Stokes equations [21], DSMC and Euler equations [21,[23][24][25], and DSMC and Navier-Stokes equations [26][27][28][29][30][31][32].…”

Unified gas kinetic scheme combined with Cartesian grid method for intermediate Mach numbers

“…We now use f BIP obtained in Equation 20 and W BIP obtained in Equation 21 as constraints to interpolate the microscopic distribution function and the macroscopic conservative variables at the interpolation (ghost) point. The coefficient vector defined in Equation 12 should be such that it must satisfy the constraint:…”

“…Higher‐order hydrodynamic equations such as Burnett and Super Burnett equations are limited to solve flows up to transition regime only . In recent years, hybrid techniques that combines both the kinetic and the NS approaches have been often used to model and simulate flows involving continuum and rarefied regimes . However, such techniques are based on the concept of zone division—the process of dividing the fluid flow domain into different regions depending on the flow regime.…”

“…often used to model and simulate flows involving continuum and rarefied regimes. [8][9][10][11][12][13][14] However, such techniques are based on the concept of zone division-the process of dividing the fluid flow domain into different regions depending on the flow regime. A buffer zone is used in such cases where it is assumed that both the kinetic and NS methods can be used.…”

Enhancing scalability of parallel structured AMR calculations

“…SAMR was originally developed to achieve higher resolution shock calculations [5,6]. Subsequent developments have expanded the SAMR algorithm space and the range of problems to which SAMR is applied, including incompressible flow [1,21]; ALE hydrodynamics [2]; particle-continuum hybrids [17,27]; flow in porous media [20]; solid mechanics [16,26]; magnetohydrodynamics [4,12,15]; laser-plasma instabilities [13]; and astrophysics [8,9].…”