Adaptive mesh refinement techniques for high-order finite-volume WENO schemes

This paper demonstrates the capabilities of Adaptive Mesh Refinement Techniques (AMR) on 2D hybrid unstructured meshes, for high order finite volume WENO methods. The AMR technique developed is a conformal adapting unstructured hybrid quadrilaterals and triangles (quads & tris) technique for resolving sharp flow features in accurate manner for steady-state and time dependent flow problems. In this method, the mesh can be refined or coarsened which depends on an error estimator, making decision at the parent level whilst maintaining a conformal mesh, the unstructured hybrid mesh refinement is done hierarchically.When a numerical method can work on a fixed conformal mesh this can be applied to do dynamic mesh adaptation. Two Refinement strategies have been devised both following a H-P refinement technique, which can be applied for providing better resolution to strong gradient dominated problems. The AMR algorithm has been tested on cylindrical explosion test and forward facing step problems

Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

In this article we present a new class of high order accurate Arbitrary-Eulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor. For that purpose, a new element--local weak formulation of the governing PDE is adopted on moving space--time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.Comment: Accepted by "Communications in Computational Physics

Large-Eddy Simulation of Axisymmetric Compression Corner Flow

The Wall-Modeled Large Eddy Simulation (WMLES) approach is used to study the interaction of a shock wave with a high Reynolds number turbulent boundary layer. Since the near wall region is modeled, high Reynolds number turbulent flows can be simulated at a moderate computational cost. The case considered is that of an axisymmetric Mach 2.85 turbulent boundary layer over a 30 compression corner. The Reynolds number of the boundary layer upstream of the interaction based on momentum thickness (Re theta = u sub infinity theta/v sub infinity) is ~12,000. The geometry and flow conditions match the experiments of Dunagan et al. (NASA TM 88227, 1986). The simulations were performed using equilibrium and non-equilibrium wall models. The agreement with experiment is encouraging for the finest grid with respect to the separation bubble length, unsteady shock structure and wall pressure distribution. Sensitivity ofWMLES results to grid, wall model, and blockage effects in the tunnel are reported

Generation of unstructured grids and Euler solutions for complex geometries

Algorithms are described for the generation and adaptation of unstructured grids in two and three dimensions, as well as Euler solvers for unstructured grids. The main purpose is to demonstrate how unstructured grids may be employed advantageously for the economic simulation of both geometrically as well as physically complex flow fields

A numerical method for junctions in networks of shallow-water channels

There is growing interest in developing mathematical models and appropriate numerical methods for problems involving networks formed by, essentially, one-dimensional (1D) domains joined by junctions. Examples include hyperbolic equations in networks of gas tubes, water channels and vessel networks for blood and lymph in the human circulatory system. A key point in designing numerical methods for such applications is the treatment of junctions, i.e. points at which two or more 1D domains converge and where the flow exhibits multidimensional behaviour. This paper focuses on the design of methods for networks of water channels. Our methods adopt the finite volume approach to make full use of the two-dimensional shallow water equations on the true physical domain, locally at junctions, while solving the usual one-dimensional shallow water equations away from the junctions. In addition to mass conservation, our methods enforce conservation of momentum at junctions; the latter seems to be the missing element in methods currently available. Apart from simplicity and robustness, the salient feature of the proposed methods is their ability to successfully deal with transcritical and supercritical flows at junctions, a property not enjoyed by existing published methodologies. Systematic assessment of the proposed methods for a variety of flow configurations is carried out. The methods are directly applicable to other systems, provided the multidimensional versions of the 1D equations are available

Aerodynamic Interference on Finned Slender Body

Aerodynamic interference can occur between high-speed slender bodies when in close proximity. A complex flowfield develops where shock and expansion waves from a generator body impinge upon the adjacent receiver body and modify its aerodynamic characteristics in comparison to the isolated case. The aim of this research is to quantify and understand the multibody interference effects that arise between a finned slender body and a second disturbance generator body. A parametric wind tunnel study was performed in which the effects of the receiver incidence and axial stagger were considered. Computational fluid dynamic simulations showed good agreement with the measurements, and these were used in the interpretation of the experimental results. The overall interference loads for a given multibody configuration were found to be a complex function of the pressure footprints from the compression and expansion waves emanating from the generator body as well as the flow pitch induced by the generator shockwave. These induced interference loads change sign as the shock impingement location moves aft over the receiver and in some cases cause the receiver body to become statically unstable. Overall, the observed interference effects can modify the subsequent body trajectories and may increase the likelihood of a collision