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ABSTRACT
A large number of numerical algorithms have been reported to solve the Euler equations of motion for a variety of mechanical and aerospace engineering applications. Based on a review of the past and current history of these solvers, a MUSCL-based solver that uses Hancock's predictor-corrector method incorporating Roe's approximate Riemann solver was found to be the most efficient second-order-accurate numerical method to solve the Euler equations. This method was subsequently extended to account for variable properties and then extensively validated for the effects of friction, heat transfer, variable area, and chemical kinetics.
This research was supported in part by the Environmental Protection Agency under Grant #F003799. It was also supported by the Ford Motor Company Dual Use Science and Technology (DUST) Simulation Based Design and Demonstration of Next Generation Advanced Diesel Technology Program funded under TACOM agreement DAAE07-01-3-0005.
Notes
*Finite-difference approximations of differential equations are obtained by solving for the exact derivative by infinite Taylor series, and then truncating the Taylor series. The terms that are truncated are called the truncation error and are represented by the order of this error: O(Δx n ). The more terms that are kept, the higher the accuracy and the higher the order.
a Includes calculations made by author.
b Modified Runge-Kutta.
c Nonhomogeneous method of characteristics.