RSICC Home Page                                                                                                                 RSICC CODE PACKAGE CCC-857

1.         NAME AND TITLE

SOPHIA: A Lagrangian-based computational fluid dynamics code for nuclear thermal hydraulics and safety applications.


The SOPHIA code is mainly a solver program. Therefore, it requires a preprocessor for input

generation and a postprocessor for data analysis.


A MATLAB script can be used for input generation. For postprocessing, the results can be

processed using ParaView since they are formatted in *.vtk.


Seoul National University, Gwanak-ro 1, Gwanak-gu, Seoul, South Korea.

Through the OECD Nuclear Energy Agency Data Bank, Issy-Les Moulineaux, France.


C++ on a LINUX or UNIX Operating System

RSICC ID: C00857MNYCP00; NEADB identifier is NEA-1911/01


The numerical methods used in nuclear safety analyses are generally mesh-based (or grid-based), such as the finite difference method (FDM), finite element method (FEM), and finite volume method (FVM). These mesh-based methods have a long history and are thus very mature both mathematically and numerically. Based on their robustness and efficiency, they dominate the CFD field and have been used in many applications, for which these methods produce very accurate results. Mesh-based methods are generally good for confined computational domains and computation in which the boundaries and interfaces do not move. However, they may not be the most efficient for modeling highly nonlinear deformation or interface regions, which are often involved in the severe accident and natural disasters related to nuclear power plants. Because of this, a multiphysics smoothed-particle hydrodynamics (SPH) code framework, SOPHIA, was recently developed at Seoul National University (SNU) that focuses on key thermal hydraulics and safety-related phenomena in nuclear reactor systems. SPH is one of the most well-known Lagrangian methods; it can handle various types of physics extensively because of its simplicity and ease of expressing and solving mathematical equations. SOPHIA is written in C++ and is parallelized using graphics processing units. Like other conventional CFD analysis codes, the applications of SOPHIA are mainly for fundamental thermal hydraulics, multiphase flow, severe accidents, natural disasters, and so on for various nuclear reactor types. Thus, the main physics behind this code include (1) fluid flow, (2) heat transfer, (3) turbulence, (4) melting/solidification, (5) multiphase, (6) natural convection, and (7) diffusion. However, in principle, the SOPHIA code can be easily extended to and is well suitable for other phenomena with some necessary modifications to the equation of state (EOS) and the physical models.


The SOPHIA code is based on SPH, which is a meshless numerical method. It solves mass, momentum, and energy conservations with the EOS and physical models in multidimensional space and time (2D/3D). The basic mathematical equations are quite similar to conventional CFDcode, except that the equations are solved in a Lagrangian framework.


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


The typical run time highly depends on the sizes and types of problems being solved. Lagrangian‑based numerical methods generally require a large amount of computational time. It may take a couple of minutes to a couple of weeks.


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


The current SOPHIA code runs in a Linux (Ubuntu) environment. However, a Windows version can be generated with some modifications, if required.

10.       REFERENCES:

§  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., “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.


The package is transmitted digitally as a download link in .zip format. It includes reference material, documentation, source files, and sample problems. Application executables are included with the package.


Aug 2021


KEYWORDS: Lagrange equations, accident analysis, hydrodynamics, multiphase flow, safety analysis, severe accident, thermal hydraulics.