Finite Elements for Fluidynamics, Variational Formulations and Calculations for Boundary-Initial-Value Problems.
Final rept. 1 Jun 73-20 Jun 77,
TEL-AVIV UNIV (ISRAEL) DEPT OF APPLIED MATHEMATICS
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Quasi linear systems of partial differential equations with initial and boundary values are treated via an equivalent variational formulation. Finite elements with linear and bi-linear approximations are described and calculations done for heat transfer, wave propagation and transonic flow problems. A variational principle for three-dimensional systems with arbitrary constraints in which the victor Lagrange multiplier has a clear physical meaning is presented and applied to additional problems of transonic flow and anisotropic wave propagation. Further numerical tests and simulations are reported. Multi-dimensional hyperbolic systems are treated by a semi-analytic method yielding the location and time where shocks appear in initially smooth flows. Application to water waves, gas shocks and plasmadynamics are described in detail. Author
- Numerical Mathematics
- Fluid Mechanics