Computational fluid dynamics based on the method of space-time conservation element and solution element

Computational Fluid Dynamics (CFD) has been used as an important tool in aerospace engineering and other fields since 1960. The applicability and efficiency of the computational techniques in CFD have been greatly improved with the rapid development of larger and faster computers. In today's CFD, some well-established traditional methods, such as the finite difference, finite volume, and finite element methods, have been utilized popularly in aerospace industry, research centers and universities. However, with the increasing demand for solving practical problems, some of the limitations and disadvantages of the traditional computational methods have been exposed.;A new method named space-time conservation element and solution element (CE/SE) method was conceived and designed from a physicist's perspective by Chang in 1991. This method is substantially different from the traditional methods in both concept and methodology. Its development is guided by the preliminary physical requirements which are needed to overcome several major shortcomings of the traditional methods. Simplicity, generality, and accuracy weigh heavily in its design. Good agreements have been observed between experiments and many of the computed CE/SE results.;The purpose of this work is to broaden the applicability of the CE/SE method and for furthering its maturity to become a robust computational fluid dynamic tool. The one- and two-dimensional Euler solvers constructed by Chang were originally used to solve 1-D problems in an infinitely long shock tube and 2-D problems in a rectangular physical domain. These solvers have been improved and new schemes have been developed in the present work, aiming at the removal of many geometric restrictions so that the applications of the CE/SE method can now be extended to solve much more complex flow problems. The major achievements reported here include (a) the proper implement of reflective boundary conditions for both one- and two-dimensional Euler solvers; (b) the extension of the CE/SE method from cartesian to cylindrical coordinates; and (c) the reconstruction of the numerical schemes to accommodate curved surfaces or bodies.;By solving a variety of flow problems, the modified as well as the newly constructed Euler solvers are validated by comparison with experiments and/or numerical solutions based on traditional numerical methods. The results computed using the CE/SE method consistently exhibit its inherent advantages of simplicity, generality, and accuracy, especially its ability to accurately capture strong curved shock waves and contact surfaces without employing any ad hoc numerical tuning techniques.