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 leastsquares type variational formulation is applied to firstorder systems to obtain an equivalent system of secondorder 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