Stable and High-Order Finite Difference Methods for Multiphysics Flow Problems

摘要: Partial differential equations (PDEs) are used to model various phenomena in nature and society, ranging from the motion of fluids electromagnetic waves stock market traffic jams. There many methods for numerically approximating solutions PDEs. Some most commonly ones finite volume method, element difference method. All have their strengths weaknesses, it is problem at hand that determines which method suitable. In this thesis, we focus on conceptually easy understand, has high-order accuracy, can be efficiently implemented computer software.We use summation-by-parts (SBP) form, together with a weak implementation boundary conditions called simultaneous approximation term (SAT). Together, SBP SAT provide technique overcoming drawbacks The SBP-SAT derive energy stable schemes any linearly well-posed initial value problem. stability not restricted by order as long numerical scheme written form. extended interfaces either domain decomposition geometric flexibility, or coupling different physics models.The contributions thesis twofold. first part, papers I-IV, develops interface procedures computational fluid dynamics problems, particular problems related Navier-Stokes conjugate heat transfer. second V-VI, utilizes duality construct only stable, but also dual consistent. Dual consistency alone ensures superconvergence linear integral functionals discretizations. By simultaneously considering well-posedness primal new advanced derived. based imposed SATs, construction continuous ensure stability, consistency, functional schemes.