NEA-1911 SOPHIA.

SOPHIA

The numerical methods used in nuclear safety analyses are generally based on mesh-based (or grid-based) methods, such as finite difference method (FDM), finite element method (FEM), and finite volume method (FVM). These mesh-based methods have a long history and thus are very mature both mathematically and numerically. Based on their robustness and efficiency, they dominated the CFD field and have been applied to many applications where these methods produce very accurate results. The mesh-based methods are generally good for confined computational domains and computation where the boundaries and interfaces are not moving. However, they may not be the most efficient for modeling highly nonlinear deformation or interface region which are often involved in the severe accident and natural disasters in nuclear power plant. Under this background, a multi-physics SPH code framework (named as SOPHIA) has been recently developed in Seoul National University (SNU) focusing on key thermal-hydraulics and safety-related phenomena in nuclear reactor systems. The smoothed particle hydrodynamics (SPH) is one of the best-known Lagrangian methods, which can extensively handle various types of physics because of its simplicity and ease in expressing and solving mathematical equations. This code is written in C++ and parallelized using GPUs. The applications of this code is mainly on fundamental thermal-hydraulics, multi-phase flow, severe accidents, natural disasters, etc. for various nuclear reactor types like other conventional CFD analysis codes. Thus, the main physics behind this code includes: (1) fluid flow, (2) heat transfer, (3) turbulence, (3) melting/solidification, (4) multi-phase, (5) natural convection, (6) diffusion, etc. However, in principle, the SOPHIA code can be easily extended to and is well suitable for other phenomena with some necessary modifications in the equation-of-state (EOS) and the physical models.

The SOPHIA code is based on the smoothed particle hydrodynamics (SPH), which is a meshless numerical method. It solves mass, momentum, energy conservations with equation-of-state (EOS) and physical models in multi-dimensional space and time (2-D/3-D). Basic mathematical equations are quite similar to the conventional computational fluid dynamics (CFD) code except that the equations are solved in a Lagrangian framework.

There is no limitations of the number of particles (the size of the problems) if the GPU memory is sufficiently available. For a single GPU, the maximum number of particles would be 10 to 15 million.

It highly depends on the sizes and the types of the problems. Lagrangian-based numerical methods generally requires large computational time. It may take a couple of minutes to a couple of weeks.

Compared to the exiting and conventional grid-based approaches, SOPHIA code can be very effective in handling physical phenomena with large non-linear deformation and complexity due to its inheriting Lagrangian Nature. They would include Tsunami, multi-phase flow, severe accidents (FCI, MCCI, corium spreading, IVMR), etc. However, the SOPHIA code is a general purpose code. Therefore, it would be able to cover a variety of fields and problems through continuous further modification and improvement. (The simulation examples can be seen in the following link: https://snueslab.com/).

The SOPHIA code is mainly a solver program. Therefore, it requires a pre-processor for input generation and a post-processor for data analysis. In our laboratory, we use a MATLAB script for input generation. For post-processing, the results can be processed using ParaView since they are formatted in *.vkt.

• Park, S.H., Jo, Y.B., Kim, E.S., Development of Multi-GPU-Based Smoothed Particle Hydrodynamics Code for Nuclear Thermal-hydraulics and Safety: Potential and Challenges, Frontiers in Energy Research, Vol. 8, 2020.

• Jo, Y.B., Park, S.H., Choi, H.Y., Jung, H.W., Kim, Y.J., Kim, E.S., SOPHIA: Development of Lagrangian-based CFD Code for Nuclear Thermal-Hydraulics and Safety Applications, Annals of Nuclear  Energy, Vol. 124, pp. 132-149, 2019.

• Park, S.H., Choi, T.S., Choi, H.Y., Jo, Y.B., Kim, E.S., Simulation of a Laboratory-scale Experiment for Wave Propagation and Interaction with a Structure of Undersea Topography near a Nuclear Power Plant using a Divergence-Free SPH, Annals of Nuclear Energy, Vol. 122, pp. 340-351, 2018.

• Park, S.H., Jo, Y.B., and Kim, E.S., High Resolution 3-D Simulation of Melt Jet Break-up Phenomenon using Multi-GPU-based Smoothed Particle Hydrodynamics Code and Comparison with Experimental Result, ICONE-28, August 2-6, Anaheim, USA, 2020.

• Jo, Y.B., and Kim, E.S., Numerical Simulation on LMR Molten-Core Centralized Sloshing Behaviors with Single/Multi-Phase Smoothed Particle Hydrodynamics Based on Novel Density Formulation, NURETH-18, August 18-23, 2019 Portland, Oregon, USA, 2019.

• Ahn, Y., Jo, Y.B., Park, S.H., Kim, J.W., and Kim, E.S., SPH Simulation on Single Bubble Behavior in Linear Shear Flow, NURETH-18, August 18-23, 2019 Portland, Oregon, USA, 2019.

• Park et al., a Development of SOPHIA-MARS Integrated Code Based on Smoothed Particle Hydrodynamics Method and Preliminary Simulation on In-Vessel Retention and External Reactor Vessel Cooling, Transactions of the Korean Nuclear Society Spring Meeting Jeju, Korea, May 21-22, 2020.

• Chae et al., Simulation of Jet Break-up in Complicated Structure in BWR Lower Plenum using Smoothed Particle Hydrodynamics, Transactions of the Korean Nuclear Society Spring Meeting Jeju, Korea, May 21-22, 2020.

SOPHIA code is parallelized using GPUs. Therefore, to run this code, a GPU card should be installed with CUDA library.

The current SOPHIA code runs in LINUX (UBUNTU) environment. However, Windows version may be generated with some modifications if required.

To run the SOPHIA code in other operating system such as Windows, some incompatible syntax should be corrected. The performance of the code in other operating systems is not guaranteed since it is currently optimized in LINUX environment.

PI: Eung Soo Kim (Professor of Seoul National University)

Co-Developers: Young Beom Jo, So Hyun Park, Hae Yoon Choi, Tae Soo Choi, Su-San Park, Hee Sang Yoo, Yelyn Ahn, Jin Hyun Kim, Tae Hoon Lee, Hoon Chae, Jin Woo Kim, Joo Ryong Park, Do Hyun Kim

Postal Address:

32-207 Department of Nuclear Engineering

Seoul National University, Gwanak-ro 1, Gwanak-gu

Seoul, South Korea (08826)