• Journal of computational fluids engineering
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• v.18 no.3
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• pp.79-86
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• 2013

Preconditioned compressible Navier-Stokes equations are solved for almost incompressible flows. Unstructured meshes are utilized for spatial discretization of complex flow domain. Effectiveness of the current preconditioning algorithm, with respect to various Reynolds numbers and Mach numbers, is demonstrated by the solution of canonical problems for incompressible flows, e.g. driven cavity flows.

• Korea-Australia Rheology Journal
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• v.19 no.4
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• pp.211-219
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• 2007

Here we demonstrate complex transient behavior of viscoelastic liquid described numerically with the Leonov model in straight and contraction channel flow domains. Finite element and implicit Euler time integration methods are employed for spatial discretization and time marching. In order to stabilize the computational procedure, the tensor-logarithmic formulation of the constitutive equation with SUPG and DEVSS algorithms is implemented. For completeness of numerical formulation, the so called traction boundaries are assigned for flow inlet and outlet boundaries. At the inlet, finite traction force in the flow direction with stress free condition is allocated whereas the traction free boundary is assigned at the outlet. The numerical result has illustrated severe forward-backward fluctuations of overall flow rate in inertial straight channel flow ultimately followed by steady state of forward flow. When the flow reversal occurs, the flow patterns exhibit quite complicated time variation of streamlines. In the inertialess flow, it takes much more time to reach the steady state in the contraction flow than in the straight pipe flow. Even in the inertialess case during startup contraction flow, quite distinctly altering flow patterns with the lapse of time have been observed such as appearing and vanishing of lip vortices, coexistence of multiple vortices at the contraction comer and their merging into one.

• JSTS:Journal of Semiconductor Technology and Science
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• v.17 no.2
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• pp.288-293
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• 2017

Transient simulation capability with an implicit time derivation method is a missing feature in deterministic Boltzmann equation solvers. The H-transformation, which is critical for the stable simulation of nanoscale devices, introduces difficulties for the transient simulation. In this work, the transient simulation of graphene sheets is reported. It is shown that simulation of homogeneous systems can be done without abandoning the H-transformation, as much as a specially designed discretization method is employed. The AC mobility and step response of the graphene sheet on the $SiO_2$ substrate are simulated.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.172-177
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• 2000

In this numerical work, three dimensional supersonic laminar flow and heat transfer of a blunt body(sphere-cone) at Mach 5 is simulated. The effects of angle of attack and the spin rate on the now and heat transfer are analysed. To solve the three dimensional compressible Wavier-Stokes equation, a finite volume method with the modified LDFSS scheme is employed for spatial discretization, and a point SGS implicit method is used for time integration. It is found that the heat transfer rate increases at the windward side and decreases at the leeward side with the angle of attack. The heat transfer rate at all surfaces slightly increases with the spin rate.

• 한국전산유체공학회:학술대회논문집
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• 2003.10a
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• pp.263-265
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• 2003

The aerodynamic performance of a shrouded tail rotor in hover has been studied by using a compressible inviscid flow solver on unstructured meshes. The numerical method is based on a cell­centered finite-volume discretization and an implicit Gauss-Seidel time integration. The results show that the performance of an isolated rotor without shroud compares well with experiment. In the case of a shrouded rotor, correction of the collective pitch angle is made such that the overall performance matches with experiment to account for the uncertainties of the experimental model configuration. Details of the flow field compare well with the experiment confirming the validity of the present method.

• Bulletin of the Korean Mathematical Society
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• v.57 no.1
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• pp.219-244
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• 2020

In this paper, we approximate the solution of the coupled nonlinear Schrödinger equations by using a fully discrete finite element scheme based on the standard Galerkin method in space and implicit midpoint discretization in time. The proposed scheme guarantees the conservation of the total mass and the energy. First, a priori error estimates for the fully discrete Galerkin method is derived. Second, the existence of the approximated solution is proved by virtue of the Brouwer fixed point theorem. Moreover, the uniqueness of the solution is shown. Finally, convergence orders of the fully discrete Crank-Nicolson scheme are discussed. The end of the paper is devoted to some numerical experiments.

• Journal of Biosystems Engineering
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• v.22 no.4
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• pp.459-468
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• 1997

To optimize the design and operation of a soil- air heat exchanger system, the effects of variables characterizing system design and operation on the performance of the system were analyzed by a theoretical model which included the three-dimensional transient heat conduction equation. The solution of the theoretical model was acquired by a computer program that uses Finite Difference Methods and Gauss-Seidel iteration computation, in which the time discretization scheme was an implicit difference appoximation. The computer program was validated first by comparison of the results for different grid sizes. Air outlet temperature, energy gain, and heat exchange efficiency of the system were analyzed based upon the tube diameter, tube length, tube thickness, and tube thermal diffusivity.

• Proceedings of the Korean Society of Propulsion Engineers Conference
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• 2004.03a
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• pp.528-531
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• 2004

For a simple one-dimensional ignition problem a mathematical model is described to investigate the difficulties in numerical simulations. Some computation results are obtained and comparison is made with analytical solution. Discussions are made on topics such as 1) coordinate transformation, 2) gas-phase and solid-phase analysis; (divergence form of the governing system, a finite-volume discretization, implicit time integration, upwind split flux, spatial accuracy improvement are described. Mass, reagent mass, and energy conservations are solved.), and 3) method to determine quantities on the burning surface (matching). Results obtained for small values of the non-dimensional pressure show a steady-combustion and good agreement with the analytical solution. Numerical instability appeared for larger values of the pressure, discussion on the cause of the problem is made. This effort is a part of a study of flame spread phenomena on solid propellant surface.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• v.19 no.2
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• pp.197-215
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• 2015

Modeling water flow in variably saturated, porous media is important in many branches of science and engineering. Highly nonlinear relationships between water content and hydraulic conductivity and soil-water pressure result in very steep wetting fronts causing numerical problems. These include poor efficiency when modeling water infiltration into very dry porous media, and numerical oscillation near a steep wetting front. A one-dimensional finite element formulation is developed for the numerical simulation of variably saturated flow systems. First order backward Euler implicit and second order Crank-Nicolson time discretization schemes are adopted as a solution strategy in this formulation based on Picard and Newton iterative techniques. Five examples are used to investigate the numerical performance of two approaches and the different factors are highlighted that can affect their convergence and efficiency. The first test case deals with sharp moisture front that infiltrates into the soil column. It shows the capability of providing a mass-conservative behavior. Saturated conditions are not developed in the second test case. Involving of dry initial condition and steep wetting front are the main numerical complexity of the third test example. Fourth test case is a rapid infiltration of water from the surface, followed by a period of redistribution of the water due to the dynamic boundary condition. The last one-dimensional test case involves flow into a layered soil with variable initial conditions. The numerical results indicate that the Crank-Nicolson scheme is inefficient compared to fully implicit backward Euler scheme for the layered soil problem but offers same accuracy for the other homogeneous soil cases.

• Journal of the Korean Society for Aeronautical & Space Sciences
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• v.30 no.8
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• pp.37-45
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• 2002

A two-dimensional unsteady, inviscid flow solver has been developed for the simulation of airfoil-vortex interactions on unstructured dynamically adapted meshes. The Euler solver is based on a second-order accurate implicit time integration using a point Gauss-Seidel relaxation scheme and a dual time-step subiteration. A vertex-centered, finite-volume discretization is used in conjunction with the Roe's flux-difference splitting. An unsteady solution-adaptive dynamic mesh scheme is used by adding and deleting mesh points to take account of both spatial and temporal variations of the flow field. The effect of vortex interaction on the aeroelastic displacement of an airfoil attached to the idealized two degree-of-freedom spring system is investigated.