• Journal of computational fluids engineering
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• v.10 no.1
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• pp.99-106
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• 2005

Performance of first, second and third order accurate methods for calculation of in viscid fluxes in fluid flow governing equations are investigated here. For the purpose, an upwind method based on Roe's scheme is used to solve 2-dimensional Euler equations. To increase the accuracy of the method two different schemes are applied. The first one is a second and third order upwind-based algorithm with the MUSCL extrapolation Van Leer (1979), based on primitive variables. The other one is an upwind-based algorithm with the Chakravarthy extrapolation to the fluxes of mass, momentum and energy. The results show that the thickness of shock layer in the third order accuracy is less than its value in second order. Moreover, applying limiter eliminates the oscillations near the shock while increases the thickness of shock layer especially in MUSCL method using Van Albada limiter.

• Communications of the Korean Mathematical Society
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• v.17 no.1
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• pp.103-120
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• 2002

A second order upwind method for linear hyperbolic systems is studied in this paper. The method approximates solutions as piecewise linear functions, and state variables and slopes of the linear functions for next time step are computed separately. We present a new method for the computation of slopes, derived from an upwinding difference for a derivative. For nonoscillatory solutions, a monotonicity algorithm is also proposed by modifying an existing algorithm. To validate our second order upwind method, numerical results for linear advection equations and linear systems for elastic and acoustic waves are given.

• 한국전산유체공학회:학술대회논문집
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• 2002.10a
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• pp.95-102
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• 2002

Studies of the numerical characteristics of implicit upwind schemes, such as upwind ADI, Line Gauss-Seidel(LGS) and Point Gauss-Seidel(LU) algorithms, for preconditioned Navier-Stokes equations ate performed. All the algorithms are expressed in approximate factorization form and Von Neumann stability analysis and convergence studies are made. Preconditioning is applied for efficient convergence at low Mach numbers and low Reynolds numbers. For high aspect ratio computations, the ADI and LGS algorithms show efficient and uniform convergence up to moderate aspect ratio if we adopt viscous preconditioning based on min- CFL/max- VNN time-step definition. The LU algorithm, on the other hand, shows serious deterioration in convergence rate as the grid aspect ratio increases. Computations for practical applications also verify these results.

• Kyungpook Mathematical Journal
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• v.61 no.2
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• pp.309-322
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• 2021

A conservative scheme for solving scalar hyperbolic equations is presented using a quadrature rule and an ODE solver. This numerical scheme consists of an upwind part, plus a correction part which is derived by introducing a new variable for the given hyperbolic equation. Furthermore, the stability and accuracy of the derived algorithm is shown with numerous computations.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.29 no.6 s.237
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• pp.703-710
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• 2005

A finite element discretization of the advection and redistancing equations of level set method has been studied. It has been shown that Galerkin spatial discretization combined with Crank-Nicolson temporal discretization of the advection equation of level set yields a good result and that consistent streamline upwind Petrov-Galerkin(CSUPG) discretization of the redistancing equation gives satisfactory solutions for two test problems while the solutions of streamline upwind Petrov-Galerkin(SUPG) discretization are dissipated by the numerical diffusion added for the stability of a hyperbolic system. Furthermore, it has been found that the solutions obtained by CSUPG method are comparable to those by second order ENO method.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.27 no.8
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• pp.1122-1133
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• 2003

Numerical characteristics of implicit upwind schemes, such as upwind ADI, line Gauss-Seidel (LGS) and point Gauss-Seidel (LU) algorithms, for Navier-Stokes equations have been investigated. Time-derivative preconditioning method was applied for efficient convergence at low Mach/Reynolds number regime as well as at large grid aspect ratios. All the algorithms were expressed in approximate factorization form and von Neumann stability analysis was performed to identify stability characteristics of the above algorithms in the presence of high grid aspect ratios. Stability analysis showed that for high aspect ratio computations, the ADI and LGS algorithms showed efficient damping effect up to moderate aspect ratio if we adopt viscous preconditioning based on min-CFL/max-VNN time-step definition. The LU algorithm, on the other hand, showed serious deterioration in stability characteristics as the grid aspect ratio increases. Computations for several practical applications also verified these results.

• 한국전산유체공학회:학술대회논문집
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• 2000.05a
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• pp.184-190
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• 2000

A well-known pressure correction method, a SIMPLE algorithm is extended to treat compressible flows. Collocated grids are used and density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm. The first-order Upwind and high-order Quick scheme are compared with respect to an accuracy and convergence time at all speeds. The extended method is verified on a number of test cases and the results we compared with other numerical results available in the literature. The calculated results show that the Quick scheme improves accuracy at all speed and also reduces the calculation time at supersonic flows, compared with the Upwind scheme.

• Journal of computational fluids engineering
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• v.5 no.2
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• pp.1-8
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• 2000

A well-known pressure correction method, a SIMPLE algorithm, is extended to treat compressible flows. Collocated grids are used and density is linked to pressure via an equation of state. The influence of pressure on density in the case of compressible flows is implicitly incorporated into the extended SIMPLE algorithm. The first-order Upwind and high-order Quick scheme are compared with respect to an accuracy and convergence time at all speeds. The extended method is verified on a number of test cases and the results are compared with other numerical results available in the literature. The calculated results show that the Quick scheme improves accuracy at all speed and also reduces the calculation time at supersonic flows, compared with the Upwind scheme.

• Journal of Mechanical Science and Technology
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• v.20 no.10
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• pp.1741-1752
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• 2006

A combined Streamline Upwind Petrov-Galerkin method (SUPG) and segregated finite element algorithm for solving conjugate heat transfer problems where heat conduction in a solid is coupled with heat convection in viscous fluid flow is presented. The Streamline Upwind Petrov-Galerkin method is used for the analysis of viscous thermal flow in the fluid region, while the analysis of heat conduction in solid region is performed by the Galerkin method. The method uses the three-node triangular element with equal-order interpolation functions for all the variables of the velocity components, the pressure and the temperature. The main advantage of the presented method is to consistently couple heat transfer along the fluid-solid interface. Four test cases, which are the conjugate Couette flow problem in parallel plate channel, the counter-flow in heat exchanger, the conjugate natural convection in a square cavity with a conducting wall, and the conjugate natural convection and conduction from heated cylinder in square cavity, are selected to evaluate efficiency of the presented method.

• Transactions of the Korean Society of Mechanical Engineers
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• v.18 no.3
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• pp.653-661
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• 1994

In this paper the CSCM type upwind flux difference splitting Navier-Stokes method has been applied to study the ARL-SL19 supersonic/transonic compressor cascade flow. H-type grid was chosen for its simplicity in applying cyclic tridiagonal matrix algorithm along with conventional slip/no-slip boundary conditions. The thin-layer algebraic model of Baldwin-Lomax was employed for the calculation of turbulent flows. The test case inlet Mach No. was 1.612 and inlet/exit pressure ratio($P_2/P_1$) was 2.15. The results were compared with experimental results from current method were compared well in suction surface with the experiments and other computational results; however, not well in pressure surface. It might be due to the complex flowfields such as shock/boundary layer interaction, turbulence, and flow separation, etc. In the future, a proper turbulence modelling and adaptive grid system will be studied to improve the solution quality.