# Toward Reduction of Conservation Equations in Curvilinear Coordinate Systems into a Set of ODEs Using the Method of Characteristics

## Abstract

This work examined the conservation equations in curvilinear coordinates using the method of characteristics. The method is commonly applied to solve first-order partial differential equations. When applying this method to the conservation laws, the main difficulty is mass and momentum equations which are simultaneous and nonlinear PDEs. The method utilizes the separation of order in order to solve the problem. The resulting nonlinear ODEs in the main equation and characteristic variables were performed by the implementation of the system of Riccati and polynomial equation. The system of polynomial and Riccati equation is handled by the proposed method to solve each polynomial and Riccati equation. Both results were then equated to define each ODE solution. The procedure was then repeated sequentially to reach the final solutions for velocities, pressure, and temperature.

## Keywords

Method of characteristics Conservation equations Reduction of PDEs Analytical solutions Curvilinear coordinates## References

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