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A new adaptive mesh refinement strategy that is based on a coupled feature-detection and error-estimation approach is developed. The overall goal is to apply the proper degree of refinement to key vortical features in aircraft and rotorcraft wakes. The refinement paradigm is based on a two-stage process wherein the vortical regions are initially identified for refinement using feature-detection, and then the appropriate resolution is determined by the local solution error. The feature-detection scheme uses a local normalization procedure that allows it to automatically identify regions for refinement with threshold values that are not dependent upon the convective scales of the problem. An error estimator, based on the Richardson Extrapolation method, then supplies the identified features with appropriate levels of refinement. The estimator is shown to be well-behaved for steady-state and time-accurate aerodynamic flows. The above strategy is implemented within the Helios code, which features a dual-mesh paradigm of unstructured grids in the near-body domain, and adaptive Cartesian grids in the off-body domain. A main objective of this work is to control the adaption process so that high fidelity wake resolution is obtained in the off-body domain. The approach is tested on several theoretical and practical vortex-dominated flow-fields in an attempt to resolve wingtip vortices and rotor wakes. Accuracy improvements to rotorcraft performance metrics and increased wake resolution are simultaneously documented.
A new adaptive mesh refinement strategy that is based on a coupled feature-detection and error-estimation approach is developed. The overall goal is to apply the proper degree of refinement to key vortical features in aircraft and rotorcraft wakes. The refinement paradigm is based on a two-stage process wherein the vortical regions are initially identified for refinement using feature-detection, and then the appropriate resolution is determined by the local solution error. The feature-detection scheme uses a local normalization procedure that allows it to automatically identify regions for refinement with threshold values that are not dependent upon the convective scales of the problem. An error estimator, based on the Richardson Extrapolation method, then supplies the identified features with appropriate levels of refinement. The estimator is shown to be well-behaved for steady-state and time-accurate aerodynamic flows. The above strategy is implemented within the Helios code, which features a dual-mesh paradigm of unstructured grids in the near-body domain, and adaptive Cartesian grids in the off-body domain. A main objective of this work is to control the adaption process so that high fidelity wake resolution is obtained in the off-body domain. The approach is tested on several theoretical and practical vortex-dominated flow-fields in an attempt to resolve wingtip vortices and rotor wakes. Accuracy improvements to rotorcraft performance metrics and increased wake resolution are simultaneously documented.
Process intensification aims for increasing efficiency and sustainability of (bio-)chemical production processes. This book presents strategies for improving fluid separation such as reactive distillation, reactive absorption and membrane assisted separations. The authors discuss computer simulation, model development, methodological approaches for synthesis and the design and scale-up of final industrial processes.
In this comprehensive volume a treatment of grid generation, adaptive refinement, and redistribution techniques is developed together with supporting mathematical, algorithmic, and software concepts. Efficient solution strategies that exploit grid hierarchies are also described and analyzed. Emphasis is on the fundamental ideas, but the presentation includes practical guidelines for designing and implementing grid strategies.
Dynamic mesh adaptation strategies are investigated. These include software development, dynamically adaptive mesh schemes, errors arising from generalized mappings and orthogonality. The strategies developed are tested against the euler and viscous Burgers Equations.
A comprehensive study of discontinuous finite element based high-order methods has been performed in this thesis, addressing a wide range of important issues related to high-order methods. The thesis starts with a detailed discussion of nodal based high-order methods and careful analysis of their stability properties. In particular, the formulations of nodal Discontinuous Galerkin method, Spectral Difference method, and Flux Reconstruction method for the scalar conservation laws are discussed first. The differences and similarities among these high-order schemes are carefully examined and effectively used to establish the linear stability of these methods. Stability proofs of nodal Discontinuous Galerkin method, Spectral Difference method, and Flux Reconstruction method subsequently lead to a new type of energy stable high-order scheme called Energy Stable Flux Reconstruction scheme. The extension of this new scheme from linear advection equation to the diffusion equation is formulated and discussed. The fundamental study of the high-order methods for scalar conservation laws lays the theoretical foundation for the subsequent extension to include conservation laws for fluid dynamics. The formulation of spectral difference method for the Navier-Stokes equations is first discussed. Validation tests to verify the resulting flow solver are presented. The extension of the spectral difference based Navier-Stokes flow solver from static fixed computational mesh to include dynamic moving deforming mesh is discussed next. An efficient mesh deformation algorithm that can handle substantial boundary movement is proposed and examined. The invariance of conservation laws mapping between coordinate systems allows the high-order scheme to be formulated on dynamic deforming meshes without deteriorating the formal order of accuracy of the underlying scheme. Detailed formulation, analysis, and validation results are presented. As a result of mesh deformation, the issue of geometric conservation needs to be addressed. The definition and origin of the geometric conservation law are discussed. The differential form of the geometric conservation law is derived from first principles for both the scalar conservation law and the fluid dynamic conservation laws. Subsequently a geometric conservative high-order scheme is formulated. The significance of geometric conservation on the stability and accuracy of the flow solution is examined. Finally a wide range of interesting fluid dynamic phenomena have been studied using the resulting high-order flow solver based on dynamic unstructured meshes. The representative test cases cover fluid dynamic phenomena ranging from completely laminar flows, to unsteady vortex dominated flows, and to flows exhibiting mixed regions of laminar, transitional, and turbulent structures. Other work that has been completed in this thesis is included in the appendix. In particular, continuous unsteady adjoint equations for advection and Burger's equations have been derived and solved using the high-order methods. The method of mesh deformation is reformulated as an optimization problem and used to achieve adaptive mesh refinement.
The last decade has seen a dramatic increase of our abilities to solve numerically the governing equations of fluid mechanics. In design aerodynamics the classical potential-flow methods have been complemented by higher modelling-level methods. Euler solvers, and for special purposes, already Navier-Stokes solvers are in use. The authors of this book have been working on the solution of the Euler equations for quite some time. While the first two of us have worked mainly on algorithmic problems, the third has been concerned off and on with modelling and application problems of Euler methods. When we started to write this book we decided to put our own work at the center of it. This was done because we thought, and we leave this to the reader to decide, that our work has attained over the years enough substance in order to justify a book. The problem which we soon faced, was that the field still is moving at a fast pace, for instance because hyper sonic computation problems became more and more important.