Keenan, Philip T.2018-06-182018-06-181991-09Keenan, Philip T.. "Thermal Simulation of Pipeline Flow." (1991) <a href="https://hdl.handle.net/1911/101732">https://hdl.handle.net/1911/101732</a>.https://hdl.handle.net/1911/101732A new numerical method for studying one dimensional fluid flow through pipelines is presented and analyzed. This work extends in a certain direction the collocation method described by Luskin ["An Approximation Procedure for Nonsymmetric, Nonlinear Hyperbolic Systems with Integral Boundary Conditions," SIAM J. Numer. Anal. 1976]. The pressure and velocity of an isothermal fluid in a pipeline can be described by a coupled pair of nonlinear first order hyperbolic partial differential equations. When thermal effects are important a third equation for temperature is added. While Luskin's method works well for the isothermal situation he discussed, it does not apply in certain common cases when thermal effects are modeled. The analysis of this new method shows how the difficulties that come from the application of standard collocation can be overcome. Experiments indicate that this method is a substantial improvement over standard collocation. It also describes an approach to analyzing nonlinear evolution equations with smooth solutions which produces convergence theorems about the nonlinear system from the corresponding linear theorems with relatively little extra work. This technique also yields an H¹ estimate in the isothermal case.54 ppengTechnical reportTR91-31