• Proceedings of the KSME Conference
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• 2002.08a
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• pp.55-58
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• 2002

Parallel finite element code has been recently developed for the analysis of the incompressible Wavier-Stokes equations using domain decomposition method. Metis and MPI libraries are used for the domain partitioning of an unstructured mesh and the data communication between sub-domains, respectively. For unsteady computation of the incompressible Navier-Stokes equations, 4-step splitting method is combined with P1P1 finite element formulation. Smagorinsky and dynamic model are implemented for the simulation of turbulent flows. For the validation performance-estimation of the developed parallel code, three-dimensional Laplace equation has been solved. It has been found that the speed-up of 40 has been obtained from the present parallel code fir the bench mark problem. Lastly, the turbulent flows around the MIRA model and Tiburon model have been solved using 32 processors on IBM SMP cluster and unstructured mesh. The computed drag coefficient agrees better with the existing experiment as the mesh resolution of the region increases, where the variation of pressure is severe.

• Journal of applied mathematics & informatics
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• v.12 no.1_2
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• pp.267-279
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• 2003

The present investigation deals with the application of Adomian's decomposition method to blood flow through a constricted artery in the presence of an external transverse magnetic field which is applied uniformly. The blood flowing through the tube is assumed to be Newtonian in character. The expressions for the two-term approximation to the solution of stream function, axial velocity component and wall shear stress are obtained in this analysis. The numerical solutions of the wall shear stress for different values of Reynold number and Hartmann number are shown graphically. The solution of this theoretical result for a particular Hart-mann number is compared with the integral method solution of Morgan and Young［17］.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.24 no.10
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• pp.1317-1325
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• 2000

A new efficient numerical method for computing three-dimensional, unsteady, incompressible flows is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used for both the diffusion and convection terms, is adopted. Based on an approximate block LU decomposition method, the velocity -pressure decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully -implicit time advancement scheme. Since the iterative procedures for the momentum equations are not required, the velocity components decouplings bring forth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to minimal channel flow unit with DNS (Direct Numerical Simulation).

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.31 no.1
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• pp.1-7
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• 2003

The aerodynamic optimization method for airfoil design was described in this paper. The Navier-Stokes equations were solved to consider the viscous flow information around an airfoil. The Modified Method of Feasible Direction(MMFD) was used for sensitivity analysis and the polynomial interpolation was used for distance calculation of the minimization. The Message Passing Interface(MPI) library of parallel computation was adopted to reduce the computation time of flow solver by decomposing the entire computational domain into 8 sub-domains and one-to-one allocating 8 processors to 8 sub-domains. The parallel computation was also used to compute the sensitivity analysis by allocating each search direction to each processor. The present optimization reduced the drag of airfoil while the lift is maintained at the tolerable design value.

• Proceedings of the KSME Conference
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• 2000.04b
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• pp.704-708
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• 2000

A new efficient numerical method for computing unsteady, incompressible flows, DRANS (Decoupled Reynolds-Averaged Navier-Stokes), is presented. To eliminate the restriction of CFL condition, a fully-implicit time advancement in which the Crank-Nicolson method is used fer both the diffusion and convection terms. is adopted. Based on decomposition method, the velocity-turbulent quantity decoupling is achieved. The additional decoupling of the intermediate velocity components in the convection term is made for the fully-implicit time advancement scheme. Since the iterative procedures for the momentum, ${\kappa}\;and\;{\varepsilon}$ equations are not required, the components decouplings bring fourth the reduction of computational cost. The second-order accuracy in time of the present numerical algorithm is ascertained by computing decaying vortices. The present decoupling method is applied to turbulent boundary layer with local forcing.

• 한국전산유체공학회:학술대회논문집
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• 1995.04a
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• pp.5-29
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• 1995

A three-dimensional flow field induced by two trains passing by each other inside a tunnel is studied based on the numerical simulation of the three-dimensional compressible Euler/Navier-Stokes equations formulated in the finite difference approximation. Domain decomposition method with the FSA(fortified solution algorithm) interface scheme is used to treat this moving-body problem. The computed resluts show basic characteristic of the flow field created when two trains passing by each other. History of the pressure distributions and the aerodynamic forces acting on the trains are mailnly discussed. The results indicate that the phenomenon is complicated due to the interaction of the flow induced by two trains. Strong side force occurs between the two trains when the front portion of the opposite train passes by. It fluctuates rapidly and maximum suction force occurs when two trains are aligned side by side. The results also indicate the effectiveness of the present numerical method for moving boundary problems.

• 한국전산유체공학회:학술대회논문집
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• 2002.05a
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• pp.8-15
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• 2002

For the large scale computation of turbulent flows around an arbitrarily shaped body, a parallel LES (large eddy simulation) code has been recently developed in which domain decomposition method is adopted. METIS and MPI (message Passing interface) libraries are used for domain partitioning and data communication between processors, respectively. For unsteady computation of the incompressible Wavier-Stokes equation, 4-step splitting finite element algorithm [1] is adopted and Smagorinsky or dynamic LES model can be chosen fur the modeling of small eddies in turbulent flows. For the validation and performance-estimation of the parallel code, a three-dimensional laminar flow generated by natural convection inside a cube has been solved. Then, we have solved the turbulent flow around MIRA (Motor Industry Research Association) model at $Re = 2.6\times10^6$, which is based on the model height and inlet free stream velocity, using 32 processors on IBM SMP cluster and compared with the existing experiment.

• 한국전산유체공학회:학술대회논문집
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• 1997.10a
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• pp.23-28
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• 1997

A parallel implementation is made of a two-dimensional finite volume model based on the SIMPLER. The solution domain is decomposed into several subdomains and the solution at each subdomain is acquired by parallel use of multiple processors. Communications between processors are accomplished by using the standard MPI and the Cray-specific SHMEM. The parallelization method for the overall solution procedure to the Navier-Stokes equations is described in detail, The parallel implementation is validated on the Cray T3E system for a benchmark problem of natural convection in a sidewall-heated cavity. The parallel performance is assessed and the issues encountered in achieving a high-performance parallel model are elaborated.

• Journal of the Society of Naval Architects of Korea
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• v.35 no.4
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• pp.1-10
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• 1998

This paper presents a vorticity-based numerical method for analyzing an incompressible Newtonian viscous flow around an impulsively started cylinder. The Navier-Stockes equations have a natural Helmholtz decomposition. The vorticity transport equation and the pressure equation are derived from this decoupled form. The associated boundary conditions are dynamic for the vorticity and pressure variables representing the coupling relation between them and the force balance on the wall. The various numerical treatments for solving the governing equations are introduced. According to Wu et al.(1994), the boundary conditions are decoupled, keeping the dynamic relation between vorticity and pressure. The vorticity transport equation is formulated by FVM and TVD(Total Variation Diminishing) scheme is used for the convection term. An integral approach similar to the panel method is used to obtain the velocity field for a given vorticity field and the pressure field, instead of the conventional differential approaches. In the numerical process, the structured grid is generated. The results are compared to existing numerical and analytic results for the validity of the present method.

• Journal of the Society of Naval Architects of Korea
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• v.28 no.1
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• pp.60-68
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• 1991

The updated Lagrangian Finite Element Method is introduced to analyse rigid body-fluid impact problem which is characterized by incompressible Navier-Stokes equations and impact-contact conditions between free surface and rigid body. For the convenience of numerical computation, velocity fields are splinted into vicous and pressure parts, and then the governing equations and boundary conditions are decomposed in accordance with the decomposition. However, Viscous stresses acting an the solid boundaries are neglected on the assumption that very small velocity gradients may occur during extremely small time interval of the impact. Four coded quadrilateral elements are used to discretize the space domain and the fully explicit time-marching algorithm is employed with a reasonably small time step. At the beginning of each time step, contact velocity of the rigid body is computed from the momentum balance between the body and the fluid. The velocity field is then computed to satisfy the discretized equations of motions and incompressibility and contact constraints as well as an exact free surface boundary condition. At the end of each time step, the fluid domain is updated from the velocity field. In the present time stepping numerical analysis, behaviour of the free surface near the body can be observed without any difficulty which is very important in the water impact problem. The applicability of the algorithm is illustrated by a wedge type falling body problem. The numerical solutions for time-varying pressure distributions and impact loadings acting ion the surface are obtained.