• Journal of the Korean Society for Industrial and Applied Mathematics
• /
• v.20 no.3
• /
• pp.243-259
• /
• 2016

The Richards equation for water movement in unsaturated soil is highly nonlinear partial differential equations which are not solvable analytically unless unrealistic and oversimplifying assumptions are made regarding the attributes, dynamics, and properties of the physical systems. Therefore, conventionally, numerical solutions are the only feasible procedures to model flow in partially saturated porous media. The standard Finite element numerical technique is usually coupled with an Euler time discretizations scheme. Except for the fully explicit forward method, any other Euler time-marching algorithm generates nonlinear algebraic equations which should be solved using iterative procedures such as Newton and Picard iterations. In this study, lumped mass and distributed mass in the frame of Picard and Newton iterative techniques were evaluated to determine the most efficient method to solve the Richards equation with finite element model. The accuracy and computational efficiency of the scheme and of the Picard and Newton models are assessed for three test problems simulating one-dimensional flow processes in unsaturated porous media. Results demonstrated that, the conventional mass distributed finite element method suffers from numerical oscillations at the wetting front, especially for very dry initial conditions. Even though small mesh sizes are applied for all the test problems, it is shown that the traditional mass-distributed scheme can still generate an incorrect response due to the highly nonlinear properties of water flow in unsaturated soil and cause numerical oscillation. On the other hand, non oscillatory solutions are obtained and non-physics solutions for these problems are evaded by using the mass-lumped finite element method.

• 한국전산유체공학회:학술대회논문집
• /
• 1999.05a
• /
• pp.137-143
• /
• 1999

The unsteady transonic viscous flow has been analyzed over an oscillatory airfoil. The CSCM(Conservative Supra Characteristic Method) upwind flux difference splitting method and the iterative time marching scheme having first order accuracy in time and second to third order accuracy in space was applied on dynamic meshes. A steady flow field of Mach number 0.7 has been calculated for the verification of unsteady algorithm. The time-accurate unsteady calculations have been done for NACA 0012 airfoil oscillating around quarter chord about freestream Mach number 0.6 on dynamic meshes. The results have been compared with the AGARD Case 3 experimental data. The periodic characteristics have been compared with the experimental results.

• 한국전산유체공학회:학술대회논문집
• /
• 2004.10a
• /
• pp.61-64
• /
• 2004

To analyze the performance of Wind turbine of the drag force type, 3-D RANS equations were solved by the iterative time marching method on sliding multiblock grid system. The numerical flow simulations by changing blade number and pitch angle were carried out : blade number = 15, 20 circumferentially; pitch angle = $30^{\circ},\; 50^{\circ}$ radially. The torque coefficient was also calculated.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.110-115
• /
• 1998

An axisymmetric Navier-Stokes procedure has been developed to analyze the pulse jet flow in a ceramic filter unit for the dust dislodging process. Using Baldwin-Lomax turbulence model as a closure relationship, the SIAF(Scalar Implicit Approximate Factorization) algorithm together with the ${\delta}^k-Correction$ iterative time marching scheme is adopted to solve the unsteady compressible Navier-Stokes equations. After some validation tests, the code has been applied to solve the pulse jet flow and examine the effects of geometry and reservoir pressure condition on the pressure level inside the filter unit. To avoid dealing with the uncertainty of such factors as the cohesion of the collected dust and the adhesion of the dust to the medium and also to simplify the analysis, the filter wall is assumed to be impermeable. The results for various test cases are presented.

• 한국전산유체공학회:학술대회논문집
• /
• 1998.05a
• /
• pp.99-109
• /
• 1998

This paper describes the analysis of flow and aeroacoustic field around a car-like body. The governing equations, 3-D unsteady incompressible Navier-Stokes equations, are solved with the iterative time marching scheme. The Chimera grid technique has been applied to efficiently simulate the flow around the side-view mirror, After the flow field analysis has been converged, the aerodynamic noise analysis of the side-view mirror has been performed by solving Ffowcs Williams and Hawkings equation. From the present numerical simulation, the A- and C-pillar vortex are evidently shown and the aerodynamic noise level induced by the side-view mirror is predicted to about 100dB.

• International Journal of Automotive Technology
• /
• v.7 no.2
• /
• pp.139-143
• /
• 2006

As an automobile tends to be high grade, the needs for more luxurious interior and comfortable HVAC system are emerged. The defrosting ability is another major factor of the performances of HVAC system. The present work is to simulate the flow and the temperature field of cabin interior during the defrost mode. The three-dimensional incompressible Navier-Stokes equations and energy equation were solved on the multi blocked grid system by the iterative time marching method and AF scheme, respectively. The present computations were validated by the comparison of the temperature field of a driven cavity and velocity field of 1/5 model scale of an automobile. Generally good agreements were obtained. By the present computation, the complicated features of flow and temperature within the automotive cabin interior could be well understood.

• 한국전산유체공학회:학술대회논문집
• /
• 1995.10a
• /
• pp.55-63
• /
• 1995

The flow field around a high-speed train including cross-wind effects has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations in the inertial frame using the iterative time marching scheme. The governing equations are differenced with 1st-order accurate backward difference scheme for the time derivatives, 3th-order accurate QUICK scheme for the convective terms and 2nd-order accurate central difference scheme for the viscous terms. The Marker-and-Cell concept was applied to efficiently solve continuity equation, which is differenced with 2nd-order accurate central difference scheme. The 4th-order artificial damping is added to the continuity equation for numerical stability. A C-H type of elliptic grid system is generated around a high-speed train including ground. The Baldwin-Lomax turbulent model was implemented to simulate the turbulent flows. To validate the present procedure, the flow around a high speed train at constant yaw angle of $45^{\circ}\;and\;90^{\circ}$ has been simulated. The simulation shows 3-D vortex generation in the lee corner. The flow separation is also observed around the rear of the train. It has concluded that the results of present study properly agree with physical flow phenomena.

• Journal of computational fluids engineering
• /
• v.2 no.1
• /
• pp.46-53
• /
• 1997

The flow field around a three dimensional minivan-like body has been simulated. This study solves 3-D unsteady incompressible Navier-Stokes equations on a non-orthogonal curvilinear coordinate system using second-order accurate schemes for the time derivatives, and third/second-order scheme for the spatial derivatives. The Marker-and-Cell concept is applied to efficiently solve continuity equation. A H-H type of multi-block grid system is generated around a three dimensional minivan-like body. Turbulent flows have been modeled by the Baldwin-Lomax turbulent model. To validate present procedure, the flows around the Ahmed body with 12.5° of slant angle are simulated. A good agreement with other numerical results is achived. After code validation, the flows around a mimivan-like body are simulated. The simulation shows three dimensional vortex-pair just behind body. The flow separation is also observed on the rear of the body. It has concluded that the results of present study properly agreed with physical flow phenomena.

• 한국전산유체공학회:학술대회논문집
• /
• 1996.05a
• /
• pp.99-104
• /
• 1996

The jet pump is being used in many fields for several purposes because of its simple construction and easy operation. The characteristics of the geometrical variables, pressure gradient and velocity distribution of the jet pump are studied using the CFD technique. The flow calculations through a bended nozzle. a mixing chamber and a venturi are presented and phenomenological aspects are discussed. This study solve 3-D steady incompressible Navier-Stokes equations using the Iterative time marching scheme. The governing equations are differenced with 1st-order accurate backward difference scheme for the time derivatives and 3rd-order accurate QUICK scheme for the convective terms. The Mark-and-cell concept was applied efficiently to solve continuity equation, which is differenced 2nd-order accurate central differenced scheme. The 4th-order artificial damping is added to the continuity equation for numerical stability. A O-type of grid system is generated inside a nozzle and venturi of the jet pump. It has concluded that the results of present study properly agree with physical flow phenomena.

• Transactions of the Korean Society of Mechanical Engineers B
• /
• v.23 no.1
• /
• pp.43-57
• /
• 1999

The fluid flow and heat transfer in a thin liquid film are investigated numerically. The flow Is assumed to be two-dimensional laminar and surface tension is considered. The most important characteristics of this flow is the existence of a hydraulic jump through which the flow undergoes very sharp and discontinuous change. Arbitrary Lagrangian-Eulerian(ALE) method is used to describe moving free boundary and a modified SIMPLE algorithm based on streamline upwind Petrov-Galerkin(SUPG) finite element method is used for time marching iterative solution. The numerical results obtained by solving unsteady full Navier-Stokes equations are presented for planar and radial flows subject to constant wall temperature or constant wall heat flux, and compared with available experimental data. It Is discussed systematically how the inlet Reynolds and Froude numbers and surface tension affect the formation of a hydraulic jump. In particular, the effect of temperature dependent fluid properties is also discussed.