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Time-accurate simulations of the thermal interaction of flows and structures, also referred to as conjugate heat transfer (CHT), can be computationally expensive. Furthermore, given the multi-physics nature of many engineering problems, resolution of other coupled phenomena, in addition to CHT, may also be of interest. This thesis aimed at developing a flexible and efficient numerical procedure for solving unsteady (transient) conjugate heat transfer. High order time integration schemes are considered, in place of commonly used second order implicit schemes, to reduce the computational work of advancing the coupled problem in time. For flexibility, the partitioned method is adopted for solving the coupled problem. For strongly coupled problems, a strongly-coupled solution algorithm is presented where high order explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) schemes are used for time integration. For Dirichlet-Neumann conditions at the interface, stability and rate of convergence of subiterations at each stage are analyzed analytically. Based on the analysis, the domain with the higher effusivity is assigned the Neumann condition and the one with the lower effusivity the Dirichlet condition. Furthermore, the interface iterations converge with a rate approximately given by the ratio of thermal effusivities of the subdomains. For weakly coupled problems, an order preserving loosely coupled solution algorithm is presented in which a family of high order implicit-explicit (IMEX) Runge-Kutta schemes are used for time integration. The IMEX schemes consist of the ESDIRK schemes for advancing the solution in time within each subdomain, and equal order and number of stages explicit Runge-Kutta (ERK) schemes for explicit integration of part of the coupling terms. Based on a stability investigation, when the ratio of thermal effusivities of the subdomains is much smaller than unity, it is possible to take large Fourier numbers using the loosely coupled alg, Aerodynamics, Aerospace Engineering

Time-accurate simulations of the thermal interaction of flows and structures, also referred to as conjugate heat transfer (CHT), can be computationally expensive. Furthermore, given the multi-physics nature of many engineering problems, resolution of other coupled phenomena, in addition to CHT, may also be of interest. This thesis aimed at developing a flexible and efficient numerical procedure for solving unsteady (transient) conjugate heat transfer. High order time integration schemes are considered, in place of commonly used second order implicit schemes, to reduce the computational work of advancing the coupled problem in time. For flexibility, the partitioned method is adopted for solving the coupled problem. For strongly coupled problems, a strongly-coupled solution algorithm is presented where high order explicit first stage singly diagonally implicit Runge-Kutta (ESDIRK) schemes are used for time integration. For Dirichlet-Neumann conditions at the interface, stability and rate of convergence of subiterations at each stage are analyzed analytically. Based on the analysis, the domain with the higher effusivity is assigned the Neumann condition and the one with the lower effusivity the Dirichlet condition. Furthermore, the interface iterations converge with a rate approximately given by the ratio of thermal effusivities of the subdomains. For weakly coupled problems, an order preserving loosely coupled solution algorithm is presented in which a family of high order implicit-explicit (IMEX) Runge-Kutta schemes are used for time integration. The IMEX schemes consist of the ESDIRK schemes for advancing the solution in time within each subdomain, and equal order and number of stages explicit Runge-Kutta (ERK) schemes for explicit integration of part of the coupling terms. Based on a stability investigation, when the ratio of thermal effusivities of the subdomains is much smaller than unity, it is possible to take large Fourier numbers using the loosely coupled alg, Aerodynamics, Aerospace Engineering

Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of such coupled problems can be computationally expensive, we consider loosely-coupled and strongly- coupled solution algorithms in which higher order multi-stage Runge-Kutta schemes are employed for time integration. The higher order time integration schemes have the potential to improve the computational efficiency at arriving at a certain accuracy relative to the traditionally used 1st and 2nd order implicit schemes. The spatial coupling between the subdomains is realized using Dirichlet-Neumann interface conditions and the coupled domains are solved in a sequential manner at each stage (Block Gauss-Seidel). In this paper, the stability of two partitioned algorithms is analyzed by considering a one dimensional model problem. The model problem consists of two thermally coupled domains where the governing equation within each subdomain is unsteady linear heat conduction. In the loosely-coupled approach, a family of multi-stage IMEX schemes is used for time integration. By observing similarities between the second stage of the IMEX schemes and the ? scheme with ? = 0.5 (Crank-Nicolson), the stability of the partitioned algorithm in which the Crank-Nicolson scheme is used for time integration is first analyzed by applying the stability theory of Godunov-Ryabenkii. The stability of the IMEX schemes is next investigated by numerically solving the model problem and comparing the results to the conclusions of the stability analysis for the Crank-Nicolson scheme. Due to partly explicit nature of the IMEX schemes, the loosely-coupled algorithm becomes unstable for sufficiently large Fourier numbers (similar to the Crank-Nicolson scheme). When the ratio of the thermal effusivities of the coupled domains is much smaller than unity, time step restriction due to stability is sufficiently weak that computations can be perf, Aerdynamics, Wind Energy and Propulsion, Aerospace Engineering

Noting that time-accurate computations of the unsteady incompressible Navier-Stokes (INS) equations can be computationally expensive, a family of higher order implicit multi-stage time integration schemes (namely ESDIRK) is used for advancing the solution to the unsteady INS in time. The higher order time integration schemes have the potential to decrease the computational cost of obtaining engineering levels of accuracy relative to the traditionally used 2nd order implicit schemes. The finite volume method is used for spatial discretization, and co-located arrangement of the primitive variables is considered. Furthermore, an iterated PISO algorithm is used to solve the incompressible Navier-Stokes equations. By using a temporally consistent Rhie-Chow interpolation, higher order temporal accuracy in solving the INS equations on co-located grids is achieved. For a two-dimensional lid driven cavity test case, the temporal convergence of the solution is investigated, with the third and fourth order ESDIRK schemes for time integration. The results demonstrate the temporal consistency and temporal order preservation of the algorithm., Aerodynamics, Wind Energy and Propulsion, Aerospace Engineering

Thermal interaction of fluids and solids, or conjugate heat transfer (CHT), is encountered in many engineering applications. Since time-accurate computations of such coupled problems can be computationally expensive, we consider loosely-coupled and strongly- coupled solution algorithms in which higher order multi-stage Runge-Kutta schemes are employed for time integration. The higher order time integration schemes have the potential to improve the computational efficiency at arriving at a certain accuracy relative to the traditionally used 1st and 2nd order implicit schemes. The spatial coupling between the subdomains is realized using Dirichlet-Neumann interface conditions and the coupled domains are solved in a sequential manner at each stage (Block Gauss-Seidel). In this paper, the stability of two partitioned algorithms is analyzed by considering a one dimensional model problem. The model problem consists of two thermally coupled domains where the governing equation within each subdomain is unsteady linear heat conduction. In the loosely-coupled approach, a family of multi-stage IMEX schemes is used for time integration. By observing similarities between the second stage of the IMEX schemes and the ? scheme with ? = 0.5 (Crank-Nicolson), the stability of the partitioned algorithm in which the Crank-Nicolson scheme is used for time integration is first analyzed by applying the stability theory of Godunov-Ryabenkii. The stability of the IMEX schemes is next investigated by numerically solving the model problem and comparing the results to the conclusions of the stability analysis for the Crank-Nicolson scheme. Due to partly explicit nature of the IMEX schemes, the loosely-coupled algorithm becomes unstable for sufficiently large Fourier numbers (similar to the Crank-Nicolson scheme). When the ratio of the thermal effusivities of the coupled domains is much smaller than unity, time step restriction due to stability is sufficiently weak that computations can be perf, Aerdynamics, Wind Energy and Propulsion, Aerospace Engineering

Noting that time-accurate computations of the unsteady incompressible Navier-Stokes (INS) equations can be computationally expensive, a family of higher order implicit multi-stage time integration schemes (namely ESDIRK) is used for advancing the solution to the unsteady INS in time. The higher order time integration schemes have the potential to decrease the computational cost of obtaining engineering levels of accuracy relative to the traditionally used 2nd order implicit schemes. The finite volume method is used for spatial discretization, and co-located arrangement of the primitive variables is considered. Furthermore, an iterated PISO algorithm is used to solve the incompressible Navier-Stokes equations. By using a temporally consistent Rhie-Chow interpolation, higher order temporal accuracy in solving the INS equations on co-located grids is achieved. For a two-dimensional lid driven cavity test case, the temporal convergence of the solution is investigated, with the third and fourth order ESDIRK schemes for time integration. The results demonstrate the temporal consistency and temporal order preservation of the algorithm., Aerodynamics, Wind Energy and Propulsion, Aerospace Engineering

The application of higher order implicit time integration schemes to conjugate heat transfer problems is analyzed with Dirichlet-Neumann as the decomposition method. In the literature, only up to second order implicit time integration schemes have been reported while there is a potential for gaining computational efficiency using higher orders. For loose coupling of the domains, the IMEX scheme consisting of the ESDIRK scheme for integrating the governing equations within the subdomains and an ERK scheme for explicit integration of the explicit coupling terms is utilized. The IMEX scheme is analyzed for two cases. In one, the material properties of the coupled domains are the same and in the other they are different. While for both cases, the IMEX scheme preserves the design order of the time integration scheme, different stability and accuracy properties are observed for the two. Finally, the computational efficiency of the higher order IMEX schemes relative to the second order scheme is demonstrated using a test case in 2-D involving coupled conduction problem of three domains., Aerodynamics, Wind Energy & Propulsion, Aerospace Engineering

The application of higher order implicit time integration schemes to conjugate heat transfer problems is analyzed with Dirichlet-Neumann as the decomposition method. In the literature, only up to second order implicit time integration schemes have been reported while there is a potential for gaining computational efficiency using higher orders. For loose coupling of the domains, the IMEX scheme consisting of the ESDIRK scheme for integrating the governing equations within the subdomains and an ERK scheme for explicit integration of the explicit coupling terms is utilized. The IMEX scheme is analyzed for two cases. In one, the material properties of the coupled domains are the same and in the other they are different. While for both cases, the IMEX scheme preserves the design order of the time integration scheme, different stability and accuracy properties are observed for the two. Finally, the computational efficiency of the higher order IMEX schemes relative to the second order scheme is demonstrated using a test case in 2-D involving coupled conduction problem of three domains., Aerodynamics, Wind Energy & Propulsion, Aerospace Engineering