Review of Summation-by-parts schemes for initial-boundary-value problems

High-order finite difference methods are efficient, easy to program, scales well in multiple dimensions and can be modified locally for various reasons (such as shock treatment for example). The main drawback have been the complicated and sometimes even mysterious stability treatment at boundaries and interfaces required for a stable scheme. The research on summation-by-parts operators and weak boundary conditions during the last 20 years have removed this drawback and now reached a mature state. It is now possible to construct stable and high order accurate multi-block finite difference schemes in a systematic building-block-like manner. In this paper we will review this development, point out the main contributions and speculate about the next lines of research in this area

Acoustic shape optimization using energy stable curvilinear finite differences

A gradient-based method for shape optimization problems constrained by the acoustic wave equation is presented. The method makes use of high-order accurate finite differences with summation-by-parts properties on multiblock curvilinear grids to discretize in space. Representing the design domain through a coordinate mapping from a reference domain, the design shape is obtained by inversion of the discretized coordinate map. The adjoint state framework is employed to efficiently compute the gradient of the loss functional. Using the summation-by-parts properties of the finite difference discretization, we prove stability and dual consistency for the semi-discrete forward and adjoint problems. Numerical experiments verify the accuracy of the finite difference scheme and demonstrate the capabilities of the shape optimization method on two model problems with real-world relevance

A robust immersed boundary method for flow in complex geometries: study of aerosol deposition in the human extrathoracic airways

The flow and the transport of particles in the human respiratory system dictate the effectiveness of therapeutic aerosols used in inhaled drug delivery. The aerosol particles are generally inhaled through the mouth, passing by the throat before reaching the targeted areas in the lungs. Therefore, knowledge of the particle deposition in the mouth-throat region is critical in the design of effective inhalation devices for optimum delivery to the lungs. Numerical simulations offer a non-invasive and cost-effective alternative to in vivo and in vitro tests. However, accurate prediction remains a challenge for numerical models due to the complexity of the flow in the extrathoracic airways. A robust immersed boundary method for flow in complex geometries is proposed. This greatly simplifies the task of grid generation and eliminates the problems associated with grid quality that exist for boundary-fitted grid techniques. The proposed method is an extension to the momentum forcing approach onto curvilinear coordinates and applies an iterative procedure to compute the forcing term implicitly, which stabilizes the scheme for higher Reynolds numbers. The use of a curvilinear grid minimizes the number of unused cells outside the geometry and increases the efficiency of the numerical scheme. The method is validated against numerical and experimental data in the literature for a number of test cases on both Cartesian and curvilinear grids. The results show good agreement with previous studies. Direct numerical simulations were performed in a number of realistic mouth and throat geometries obtained from MRI scans. A Lagrangian particle tracking scheme was employed to advance the particles dynamically, and total and regional deposition efficiencies were determined and compared to in vitro data. The effect of inflow turbulence and intersubject variation on deposition was studied. Geometric variation has a large impact on total deposition whereas the effect of inflow turbulence is confined to oral deposition

The Sixth Copper Mountain Conference on Multigrid Methods, part 1

The Sixth Copper Mountain Conference on Multigrid Methods was held on 4-9 Apr. 1993, at Copper Mountain, CO. This book is a collection of many of the papers presented at the conference and as such represents the conference proceedings. NASA LaRC graciously provided printing of this document so that all of the papers could be presented in a single forum. Each paper was reviewed by a member of the conference organizing committee under the coordination of the editors. The multigrid discipline continues to expand and mature, as is evident from these proceedings. The vibrancy in this field is amply expressed in these important papers, and the collection clearly shows its rapid trend to further diversity and depth

ICASE/LaRC Workshop on Adaptive Grid Methods

Solution-adaptive grid techniques are essential to the attainment of practical, user friendly, computational fluid dynamics (CFD) applications. In this three-day workshop, experts gathered together to describe state-of-the-art methods in solution-adaptive grid refinement, analysis, and implementation; to assess the current practice; and to discuss future needs and directions for research. This was accomplished through a series of invited and contributed papers. The workshop focused on a set of two-dimensional test cases designed by the organizers to aid in assessing the current state of development of adaptive grid technology. In addition, a panel of experts from universities, industry, and government research laboratories discussed their views of needs and future directions in this field