• Convergence Security Journal
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• v.5 no.3
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• pp.93-97
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• 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
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• v.7 no.2
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• pp.11-16
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• 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.

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