A least squares finite element approach to unsteady gas dynamics
Abstract
A numerical method for solving unsteady gas dynamic equations is proposed. The method is based on least squares finite element components constructed in space and time. The components are identified as: (1) the construction of elements which correspond to the mathematical domain of dependence of the vertex, (2) the conversion of the differential equation into a least squares minimization problem, (3) solving a nonlinear problem by linearization and iteration, and (4) the discretization of the error integrals by using a quadrature formula involving the nodal values of the elements. The numerical accuracy of the technique is determined by comparison of numerical results to a problem with a known solution.
 Publication:

International Journal for Numerical Methods in Engineering
 Pub Date:
 1978
 Bibcode:
 1978IJNME..12....3P
 Keywords:

 Finite Element Method;
 Gas Dynamics;
 Least Squares Method;
 Unsteady Flow;
 Velocity Distribution;
 Differential Equations;
 Error Analysis;
 Gas Flow;
 Iterative Solution;
 Linearization;
 Nonlinear Equations;
 Quadratures;
 Fluid Mechanics and Heat Transfer