Computational Engineering

High-performance computing to solve multiphysics engineering problems

Many of the actual problems in the engineering fields, like civil engineering, are generally the simultaneous combinations of multiple physical phenomena, which are called multiphysics problems. The examples can be found in the fluid structure interaction (FSI), fluid mechanics with transfer of heat and material, non-Newtonian fluids related to rheological properties and so on. While these multiphysics problems have been difficult to deal with, recent advancements of numerical methods and computer architecture enable us to predict a part of the problems in detail. In our Lab., we are now developing the reliable computational methods for multiphysics problems on the basis of our original computational fluid dynamics (CFD) techniques by integrating the knowledges of solid mechanics, constitutive relationships of various materials and other physical processes through the collaborative studies with the researchers in different fields.

Our research activities cover the following items: 1) derivation of governing equations and proposal of new models for multiple physical phenomena taking into account their mutual interactions, 2) development of new computational methods regarding FDM, FVM, FEM, BIEM, DEM and so on, 3) parallelization of numerical procedures with MPI and OpenMP, 4) application of the computational methods to actual engineering problems.

Academic Staff


Satoru USHIJIMAProfessor (Academic Center for Computing and Media Studies)

Research Topics

  • Computational fluid dynamics (CFD) for incompressible fluids
  • Multiphysics problems such as fluid-structure interactions
  • Parallel computation
  • Numerical visualization
  • Application of computational methods to civil engineerings


Room 219, Research Bldg. No.5, Yoshida Campus
TEL: +81-75-753-7493
FAX: +81-75-753-7493

Research Topics

Computational method for 3D incompressible fluids

Flows of water and air dealt with in civil engineering can be treated as incompressible fluids. In recent years, due to the rigorous studies on numerical methods and the advancements of computer architecture, it has come to be able to predict the various complicated behaviors of the incompressible fluids with sufficient accuracy.

In the numerical predictions for high-Reynolds-number 3D incompressible flows, it is particularly essential to take into account the following points: 1) accurate treatment of non-linear (convective or advective) terms, 2) to obtain the numerical results that satisfy conservation and incompressible conditions, and 3) to make the computational procedures efficient . In our Lab., some advanced numerical prediction methods have been developed to cope with the above subjects adequately in the collocated grid system, in which both pressure and three velocity components are defined at the same cell-center points, on the basis of the finite volume method (FVM). For example, we have proposed the fifth-order conservative scheme with quintic spline functions (FVM-QSI scheme), the flux control method that prevents numerical oscillations which consists of a direct control (DC) method and a flux potential (FP) method, the implicit method (C-ISMAC method) that is suitable to treat the pressure-gradient terms in the collocated grid system and so on. In addition, the pressure computation method (C-HSMAC method) has been proposed to deal with the two fluids, which have largely different densities such as water and air, simultaneously in the same computational space. The C-HSMAC method has been proved to be a robust numerical method and it enables us to obtain the converged results that satisfy incompressible conditions more efficiently than the usual methods, such as a SOLA method.

While the proposed methods are mainly used in the structured collocated grid systems, which are based on the orthogonal or boundary-fitted curvilinear coordinates, some of the methods are also available in the unstructured collocated grid systems. In addition, our methods have been applied to shallow-water equations and non-Newtonian fluids as well.

Iso-surfaces of vorticity in the turbulent wake behind a cylinder

Computational method for interactions between free-surface flows and solid object motions

It is important to develop the computational methods to predict the interactions between free-surface flows and the motions of solid objects included in the flows. For example, it is necessary to understand the behaviors of the floating structures exposed to coastal waves and the movements of driftwood and debris transported by the overflows of floods and Tsunamis. In addition, it is valuable to estimate the fluid forces acting on the vegetation near water-front regions and hydraulics structures as well as their deformations and destructive procedures by the flows.

In order to develop the numerical method to deal with such problems, the target field is taken as a multiphase field, consisting of gas, liquid and solid phases, and we developed a computational method, called MICS (Multiphase Incompressible flow solver with Collocated grid System). The MICS allows us to estimate the fluid forces acting on the objects by the volume integral of the pressure and viscous terms of the momentum equations in a multiphase model. Thus, the numerical procedures to treat the objects in the flows become simple and numerically robust.

On the other hand, a T-type solid model has been proposed to predict the behaviors of the solid objects moving in the fluid accompanying their collisions. In this model, an object is represented with multiple tetrahedron elements and the physical properties of the object, such as volume, mass and inertial tensors, are calculated with the elements. These elements are also utilized to estimate the fluid forces acting on the objects and other interactions with the fluid flows. In addition, the T-type solid model makes the numerical algorithms for collision detections much easier than those used in the polygon models, since the collisions and contact forces are calculated with the contact-detection-spheres (CDS) which are placed near the object surfaces on the basis of the distinct element method (DEM).

Recently, we have proposed the solid models for elastic objects that can deal with finite deformations due to the fluid forces. To develop these models, we have collaborative studies with the researchers in the solid mechanics fields as well.

(a) T-type solid model (CAD model, tetrahedron elements and CDS)

(b) Falling rectangular object in water

(c) Cubic blocks transported by wave-induced flows (T-type solid models are used for all objects)

(d) Comparison with experiments (red symbols)

(e) Wave-breaking blocks stacked in water (T-type solid models are used for objects)

(f) Driftwood gathered near slit (Driftwood are represented by T-type models)

(g) Deformations of elastic plates by free-surface sloshing motions

Parallelization of numerical procedures in CFD

High-performance computing is always necessary in CFD, especially to predict the large-scale 3D high-Reynolds-number incompressible flows. To achieve such computations, it is essential to parallelize the high-loaded numerical procedures (hot spots), such as the solution of large linear systems regarding pressure-Poisson equations, higher-accuracy schemes for non-linear terms, implicit algorithms for convection and diffusion equations and so on. While the parallelization methods depend on the available computer architecture, they are roughly classified into 1) process-parallel (MPI), 2) thread-parallel (OpenMP) and 3) hybrid parallel with 1) and 2). The numerical procedures in C-HSMAC, C-ISMAC and FVM-QSI methods have been parallelized with MPI on the basis of the domain-decomposition methods for structured and unstructured collocated grid systems. The Krylov subspace methods to solve linear systems were also parallelized with OpenMP in the shared memory system. The parallelization of the MICS to deal with the fluid-solid interactions is one of our current most important subjects.

(a) overlapping zone

(b) process-parallel (HPC2500)

(c) thread-parallel (HPC2500)

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