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Anisotropic metric-based mesh adaptation has proved its efficiency to reduce the CPU time of steady and unsteady simulations while improving their accuracy. However, its extension to time-dependent problems with body-fitted moving geometries is far from straightforward. This paper establishes a well-founded framework for multiscale mesh adaptation of unsteady problems with moving boundaries. This framework is based on a novel space–time analysis of the interpolation error, within the continuous mesh theory. An optimal metric field, called ALE metric field, is derived, which takes into account the movement of the mesh during the adaptation. Based on this analysis, the global fixed-point adaptation algorithm for time-dependent simulations is extended to moving boundary problems, within the range of body-fitted moving meshes and ALE simulations. Finally, three dimensional adaptive simulations with moving boundaries are presented to validate the proposed approach. [ABSTRACT FROM AUTHOR]

Abstract: Unstructured meshes are in widespread use throughout computational physics, but calculating diagnostics of simulations on such meshes can be challenging. For example, in geophysical fluid dynamics, it is frequently desirable to compute directional integrals such as vertical integrals and zonal averages; however, it is difficult to compute these on meshes with no inherent spatial structure. This is widely regarded as an obstacle to the adoption of unstructured mesh numerical modelling in this field. In this paper, we describe an algorithm by which one can exactly compute such directional integrals on arbitrarily unstructured meshes. This is achieved via the solution of a problem of computational geometry, constructing the supermesh of two meshes. We demonstrate the utility of this approach by applying it to a classical geophysical fluid dynamics system: the thermally driven rotating annulus. This addresses an important objection to the more widespread use of unstructured mesh modelling. [Copyright &y& Elsevier]

Abstract: Laminar-turbulent transition of hypersonic boundary layers can be affected significantly by the existence of surface roughness. Currently many important mechanisms of roughness-induced transition are not well understood. In recent years, direct numerical simulation (DNS) has been extensively applied for investigating instability and transition mechanisms of hypersonic boundary layers. Most of the past DNS studies, however, have been based on body-fitted grids for smooth surfaces without roughness. Due to complex geometry of embedded roughness, the use of body-fitted grids can be very difficult for flow with arbitrary surface roughness. In this paper, we present a new high-order cut-cell method to overcome the natural complexities in grid generation around arbitrary surface of roughness. The new method combines a non-uniform-grid finite-difference method for discrete grid points near the solid boundary and a shock-fitting method for the treatment of the bow shock. The non-uniform-grid finite-difference formulas are expressed in a general explicit form so that they can be applied to different multi-dimensional problems without any modification. The computational accuracy of new algorithms of up to O(h 4) are tested on several one- and two-dimensional elliptic equations in irregular domains. In addition, the new method is applied to the simulation of the receptivity process of a Mach 5.92 flow over a flat plate under the combined effect of an isolated surface roughness element and surface blow and suction. A good agreement is found between the unsteady flow results and those obtained by a Linear Stability Theory (LST). [ABSTRACT FROM AUTHOR]