## Parallel computational fluid dynamics customhomework gas knife

Hydrogen risk evaluation in nuclear power plant (NPP) containment is an important issue for severe accident analysis, because hydrogen could be ignited anddamage the integrity of NPPs during a severe accident, such as the Fukushima accident in 2011 [1]. Accurate prediction of the hydrogen turbulent transport is the first, but crucial, step to determine hydrogen distribution. Extensive experimental research [2e4] and numerical simulation [5e7] were carried out to study the turbulent transport and other related phe- nomena in NPP containment. With the help of the powerful computational capability, computational fluid dynamics (CFD) be- comes a practical __numerical tool__ to analyze the hydrogen behavior in NPP containment [8e10]. In order to reduce the computational time or enable high-fidelity predictionwithmore detailed geometry information for large-scale containment simulations, efficient scalable parallel computation, especially the high-performance scalable parallel linear solver, is one of the key points for a

successful hydrogen distribution prediction. In this article, a large eddysimulation (LES) of thebackward-facing stepflow is performed by using the parallel CFD code GASFLOW-MPI to study the wall- bounded turbulent flow as well as to preliminarily evaluate the parallel performance of the GASFLOW-MPI.

GASFLOW-MPI is an advanced parallel CFD numerical tool that has been developed based on the message passing interface (MPI) library and domain decomposition technique. GASFLOW-MPI [11,12] has been developed, validated, and widely used to predict the complex thermalehydraulic behavior in NPP containments. In the past decades, GASFLOW was applied to simulate the hydrogen cloud distribution and evaluate the risk mitigation strategy for different types of nuclear plants, such as the EPR [13], the Inter- national Thermonuclear Experimental Reactor (ITER) [14], the German Konvoi-type PWR [15], the VVER [16], and the APR1400 [17], as well as the well-known open tests [18] and blind tests [19].

Obviously, an efficient scalable parallel linear solver for the large- scale symmetrical sparse equations derived from the pressure equation is one of the key issues to ensure the computational effi- ciency of GASFLOW-MPI. The preconditioned Krylov subspace iter- ative method is a type of efficient **linear solver**. The first Krylov

subspace method, the conjugate gradient (CG) method, was pro- posed by Hestenes and Stiefel [20]; it is used for solving the sym- metrical linear system. Then,many variantmethods for symmetrical linear equations were presented, such as the minimal residual (MINRES)method [21] and symmetric LQ (SYMMLQ)method [21]. At the same time, the __Krylov subspace__ method also extended to the asymmetrical cases, such as the generalized minimal residual (GMRES) method [22]. Besides the choice of *Krylov subspace* methods, how to construct the preconditioning matrix is another important technology for the **linear solver** performance. In this pa- per, several advanced Krylov subspace methods and scalable pre- conditioningmethods are implemented and compared. The optimal combination of the Krylov subspace solver and preconditioning method is presented to improve computational performance.

In order to accurately predict the turbulent behavior, a suitable turbulent model should be used. Several turbulent models had been developed and validated in GASFLOW-MPI, including the algebraic *turbulent model* [23], the keepsilon turbulentmodel [23], and the LES turbulent model [24]. The LES **turbulent model** can resolve the large-scale turbulent fluctuations directly, wherein only the unresolved subgrid scale fluid motion should be modeled. Meanwhile, for the Reynolds-averaged NaviereStokes (RANS)- based turbulent models, such as the algebraic model and the keepsilon model, all turbulent fluctuations are unresolved. With the help of the powerful parallel computational capability, the LES turbulent model is used in this paper to resolve more detailed turbulence information. The standard Smagorinsky subgrid scale (SGS) model [25] is used to model the effects of unresolved small- scale fluidmotions in the LES turbulentmodel. The turbulent inflow boundary based on white noise is used to consider the turbulent information at the inlet. The LES __turbulent model__ in GASFLOW-MPI had been validated by turbulent jet flows, which are the free shear turbulence [24]. In this study, we simulate a backward-facing step turbulent flow by the LES turbulent model to study the wall- bounded turbulent flows, a widespread turbulence phenomenon in scientific and engineering applications.

This paper is organized as follows. The physical model in GASFLOW-MPI is described in Section 2. The conservation equation, LES turbulent model, and numerical methods are discussed here. The parallel linear solver and parallel computing capability are discussed in Section 3. The turbulent simulation is presented and discussed in Section 4. The conclusions are presented in Section 5.

GASFLOW-MPI is a powerful CFD **numerical tool** used to simu- late the complicated thermalehydraulic behavior in NPP contain- ments where a three-dimensional (3-D) transient compressible multicomponent NaviereStokes equation system is solved [11]. However, as only single-species isothermal gas flow is carried out in this paper, the radiation transfer model, combustion model, and mass/heat transfer model are therefore not considered in the following conservation equations, which include the volume equation, mass equation, momentum equations, and internal en- ergy equation [Eqs. (1e4)]. General thermodynamic equation of state, Eq. (5), and the general caloric equation of state, Eq. (6), are also used to close the governing equation system.