• Convergence Security Journal
• /
• v.5 no.3
• /
• pp.93-97
• /
• 2005

MacCormack's method is an explicit, second order finite difference scheme that is widely used in the solution of hyperbolic partial differential equations. Apparently, however, it has shown entropy violations under small discontinuity. This non-physical shock grows fast and eventually all the meaningful information of the solution disappears. Some modifications of MacCormack's methods follow ideas of central schemes with an advantage of second order accuracy for space and conserve the high order accuracy for time step also. Numerical results are shown to perform well for the one-dimensional Burgers' equation and Euler equations gas dynamic.

• Journal of Power System Engineering
• /
• v.7 no.2
• /
• pp.11-16
• /
• 2003

Because of the advancement of digital computers and software technologies, simulation methods have been used to reduce time and costs. A lot of simulation methods have been developed for the improvement of charging efficiency on the intake and exhaust system of engines. In this study, as a basic step for the development of the gas flow simulation program for the intake and exhaust system, the gas flow in a pipe-orifice system was calculated with three algorithms(Method of Characteristics, MacCormack Method for conservation, and MacCoramck Method for nonconservation). The calculated results using three numerical algorithms were compared with measured result to verify the calculation accuracy.

• The KSFM Journal of Fluid Machinery
• /
• v.2 no.4 s.5
• /
• pp.16-23
• /
• 1999

The characteristic of unsteady flowfields on gas turbine, particularly on a rotor blade surface has been numerically investigated. The unsteady flow in a rotor blade passage as a result of wake/blade interaction is modeled by the inviscid flow approach, and solved by Euler equations using a time accurate marching scheme. Unsteady flow in the blade passage is induced by periodically moving a wake model across the passage inlet. The wake model used in this study is the Gaussian wate model in which the wake flow is assumed to be parallel with uniform static pressure and uniform relative total enthalpy. Numerical results show that for the case of Ps/Pr=1.5, the velocity and pressure distribution on the blade surfaces have much more complex profiles than for the case of Ps/Pr=1.0.

• KSCE Journal of Civil and Environmental Engineering Research
• /
• v.9 no.1
• /
• pp.41-52
• /
• 1989

Numerical characteristics for the shallow water equation are analyzed with ADI, Hansen, Heaps, Richtmyer and MacCormack schemes. Stability, CPU time and accuracy are investigated for the linear model which has analytic solutions and circulation is simulated for the nonlinear model. The results show that ADI method has some defects in CPU time and accuracy for the computation of velocity. But ADI method simulates circulation well and has the largest stability region. Richtmyer scheme is the best among the other explicit schemes. Effective viscosity term is found to be essential for numerical experiments of the shallow water equation.

• Journal of Energy Engineering
• /
• v.6 no.1
• /
• pp.52-57
• /
• 1997

Dynamic characteristics of compressible flow fields in super-circled constricted tube have been studied numerically. By applying MacCormack's explicit scheme, time marching method with predictor/corrector step, Euler equation is solved to find characteristics of fluid flow in a constricted tube where a two-dimensional inviscid compressible flow is assumed. The effects of tube diameter and aspect ratios on the pressure variations are discussed extensively. The results of the developed numerical schemes are compared with those of commercial FLUENT code, and show a good agreement.

• Proceedings of the Korea Water Resources Association Conference
• /
• 2005.09a
• /
• pp.351-352
• /
• 2005

• Journal of the Korean Society of Hazard Mitigation
• /
• v.8 no.3
• /
• pp.23-27
• /
• 2008

The new conjunctive surface-subsurface flow model at a large scale was developed by using a 1-D Diffusion Wave (DW) model for surface flow interacting with the 3-D Volume Averaged Soil-moisture Transport (VAST) model for subsurface flow for the comprehensive terrestrial water and energy predictions in Land Surface Models (LSMs). A selection of numerical implementation schemes is employed for each flow component. The 3-D VAST model is implemented using a time splitting scheme applying an explicit method for lateral flow after a fully implicit method for vertical flow. The 1-D DW model is then solved by MacCormack finite difference scheme. This new conjunctive flow model is substituted for the existing 1-D hydrologic scheme in Common Land Model (CLM), one of the state-of-the-art LSMs. The new conjunctive flow model coupled to CLM is tested for a study domain around the Ohio Valley. The simulation results show that the interaction between surface flow and subsurface flow associated with the flow routing scheme matches the runoff prediction with the observations more closely in the new coupled CLM simulations. This improved terrestrial hydrologic module will be coupled to the Climate extension of the next-generation Weather Research and Forecasting (CWRF) model for advanced regional, continental, and global hydroclimatological studies and the prevention of disasters caused by climate changes.

• Proceedings of the Korean Society of Soil and Groundwater Environment Conference
• /
• 2003.09a
• /
• pp.213-216
• /
• 2003

Efforts for better understanding of the interaction between groundwater recharge and thermal regime of the subsurface medium is gaining momentum for its diverse applications in water resources. A numerical model is developed to simulate temperature variations of the subsurface under time varying groundwater recharge. The model utilizes MacCormack scheme for finite difference approximation of the partial differential equation describing the conductive and advective heat transport. For the estimation of recharge rate, optimization of the model is realized by searching for the unknown parameters which minimize the root-mean-square error between simulated and measured temperatures. Simulation results for 22-year time series data of temperature measurements reveal that the proposed model can accurately simulate subsurface temperature variations resulting from the redistribution of the heat due to the movement of water and it can also estimate temporal variations of recharge. Seasonal variations of recharge and a linear relationship between precipitation and recharge are clearly reflected in the simulated results.