Numerical resolution of a conservation equation by a variational approach
Abstract
The use of implicit schemes to solve the equations describing the movement of a perfect fluid in subsonic and transonic conditions is considered. A least-squares type variational formulation is applied to first-order systems to obtain an equivalent system of second-order partial derivative equations. The method is illustrated in a model problem which involves solution of the mass conservation equation in a pipe, when the velocity field is given. The approach is a first step in the solution of stationary Euler equations. Results obtained by finite element methods and finite difference methods are compared.
- Publication:
-
NASA STI/Recon Technical Report A
- Pub Date:
- 1978
- Bibcode:
- 1978STIA...7845287C
- Keywords:
-
- Conservation Equations;
- Numerical Analysis;
- Steady Flow;
- Subsonic Flow;
- Transonic Flow;
- Variational Principles;
- Finite Difference Theory;
- Finite Element Method;
- Ideal Fluids;
- Least Squares Method;
- Fluid Mechanics and Heat Transfer