Adaptive Unstructured Grids Research Articles

解適合非構造格子を用いた流れの数値計算における定常解への収束特性について : 計算格子の品質の影響(OS7 21世紀に開いた圧縮性流体力学)

解適合非構造格子を用いた流れの数値計算における定常解への収束特性について : 計算格子の品質の影響(OS7 21世紀に開いた圧縮性流体力学)

Parallel multilevel iterative linear solvers with unstructured adaptive grids for simulations in earth science

AbstractA new multigrid‐preconditioned conjugate gradient (MGCG) iterative method for parallel computers is presented. Iterative solvers with preconditioning, such as the incomplete Cholesky or incomplete LU factorization methods, represent some of the most powerful tools for large‐scale scientific computation. However, the number of iterations required for convergence by these methods increases with the size of the problem. In multigrid solvers, the rate of convergence is independent of problem size, and the number of iterations remains fairly constant. Multigrid is also a good preconditioning algorithm for Krylov iterative solvers. In this study, the MGCG method is applied to Poisson equations in the region between two spherical surfaces on semi‐unstructured, adaptively generated prismatic grids, and to grids with local refinement. Computations using this method on a Hitachi SR2201 with up to 128 processors demonstrated good scalability. Copyright © 2002 John Wiley & Sons, Ltd.

The effect of overall discretization scheme on Jacobian structure, convergence rate, and solution accuracy within the local rectangular refinement method

AbstractThe local rectangular refinement (LRR) solution‐adaptive gridding method automatically produces orthogonal unstructured adaptive grids and incorporates multiple‐scale finite differences to discretize systems of elliptic governing partial differential equations (PDEs). The coupled non‐linear discretized equations are solved simultaneously via Newton's method with a Bi‐CGSTAB linear system solver. The grids' unstructured nature produces a nonstandard sparsity pattern within the Jacobian.The effects of two discretization schemes (LRR multiple‐scale stencils and traditional single‐scale stencils) on Jacobian bandwidth, convergence speed, and solution accuracy are studied. With various point orderings, for two simple problems with analytical solutions, the LRR multiple‐scale stencils are seen to: (1) produce Jacobians of smaller bandwidths than those resulting from the traditional single‐scale stencils; (2) lead to significantly faster Newton's method convergence than the single‐scale stencils; and (3) produce more accurate solutions than the single‐scale stencils.The LRR method, including the LRR multiple‐scale stencils, is finally applied to an engineering problem governed by strongly coupled, highly non‐linear PDEs: a steady‐state lean Bunsen flame with complex chemistry, multicomponent transport, and radiation modeling. Very good agreement is observed between the computed flame height and previously published experimental data. Copyright © 2001 John Wiley & Sons, Ltd.

Computation of a Nonequilibrium Expansion Flow in a Single Expansion Ramp Nozzle

The simulation of the flow inside the propulsion system is of essential interest, for the design of airbreating hypersonic vehicles. To compute accurately the expansion flow of a hydrogen/air mixture at high temperatures, the chemical and vibrational nonequilibrium effects must be taken into account. A finite element code is used to model chemical reactions considering finite-rate chemistry and vibrational relaxations according to the Landau-Teller theory (Landau, L., and Teller, E., Zur Theorie der Schalldispersion, Physikalische Zeitschrift der Sowjetunion, Vol. 10, No. 1, 1936, pp. 34-43). The computational domain is discretized by applying unstructured adaptive grids. Different test cases are computed, and the results are compared with measured and numerical data. In one test case, a remarkable difference between the rotational and vibrational temperature of a hydrogen/air nozzle flow is seen. This difference in the experiment is also supported by the computation. Because the applied relaxation rates are small compared to other data given in literature, the thermal nonequilibrium effects gain more importance.

Evaluation of the Operational Multiscale Environment Model with Grid Adaptivity against the European Tracer Experiment

Abstract The Operational Multiscale Environment Model with Grid Adaptivity (OMEGA) is a multiscale nonhydrostatic atmospheric simulation system based on an adaptive unstructured grid. The basic philosophy behind the OMEGA development has been the creation of an operational tool for real-time aerosol and gas hazard prediction. The model development has been guided by two basic design considerations in order to meet the operational requirements: 1) the application of an unstructured dynamically adaptive mesh numerical technique to atmospheric simulation, and 2) the use of embedded atmospheric dispersion algorithms. An important step in proving the utility and accuracy of OMEGA is the full-scale testing of the model using simulations of real-world atmospheric events and qualitative as well as quantitative comparisons of the model results with observations. The main objective of this paper is to provide a comprehensive evaluation of OMEGA against a major dispersion experiment in operational mode. Therefore, O...

Morphological transformation of shock waves behind a flat plate

The interaction of a travelling shock with the shear layer of a flat plate is studied computationally. The Euler and Navier-Stokes equations are solved numerically on quadrilateral unstructured adaptive grids. The flat plate is installed horizontally on the central axis of a shock tube. The shear layer is first created by two shock waves at different speeds splitted by a flat plate. A series of small vortices is developed as a consequence in the shear layer. The shock wave reflected at the end wall impinges the shear layer. The complicated shock dynamics in the evolution to the pseudo-steady state is represented with the morphological transformation of a planar shock into an oblique shock.

1411 非構造格子を用いた非球形気泡の内部温度場に関する数値解析手法の改良(GS-5 キャビテーション)

We have improved the numerical scheme based on the boundary element method combined with the finite volume method to consider the heat transfer of internal gas in the final stage of bubble collapse. Unstructured adaptive grids are used inside the largely deformed bubble. We investigate the motion of the collapsing bubble near a plane rigid wall. The dynamics of a toroidal bubble, which is formed after the penetration of liquid microjet, are taken into account in the present analysis. The results show that the present scheme can handle the temperature fields for the toroidal bubble.

303 解適合非構造格子を用いた非定常衝撃波反射の数値シミュレーション(O.S.3-1 熱流体解析における新潮流1)(オーガナイズドセッション3 : 熱流体解析における新潮流)

303 解適合非構造格子を用いた非定常衝撃波反射の数値シミュレーション(O.S.3-1 熱流体解析における新潮流1)(オーガナイズドセッション3 : 熱流体解析における新潮流)

Numerical Analysis of Temperature Fields inside Collapsing Nonspherical Bubbles Using Unstructured Grids.

We have improved the numerical scheme based on the boundary element method combined with the finite volume method. Heat transfer inside the bubble is taken into account in this sheme. We apply unstructured adaptive grids inside the bubble, which are generated by Delaunay triangulation, to analyze the temperature field inside the collapsing bubble with the very large deformation. We compare the present numerical results with one-dimensional results for a spherical bubble and numerical results for a nonspherical bubble where the structured grids are used to calculate the heat transfer inside the bubble. The results show that the present method has sufficient accuracy to deal with thermal boundary layers both for spherical and nonspherical bubble collapses. It is also shown that the present scheme is effective for the analysis of a tiny bubble in which the thermal boundary layer near the bubble wall is relatively thick to its radius.

A Solution-Adaptive Unstructured Grid Method by Grid Subdivision and Local Remeshing

An adaptive unstructured grid refinement technique has been developed and successfully applied to several three-dimensional inviscid flow test cases. The method is based on a combination of surface mesh subdivision and local remeshing of the volume grid. Simple functions of flow quantities are employed to detect dominant features of the flowfield. The method is designed for modular coupling with various error/feature analyzers and flow solvers. Several steady-state, inviscid flow test cases are presented to demonstrate the applicability of the method for solving practical three-dimensional problems. In all cases accurate solutions featuring complex, nonlinear flow phenomena such as shock waves and vortices have been generated automatically and efficiently

Unstructured Adaptive Grid Flow Simulations of Inert and Reactive Gas Mixtures

Unstructured adaptive grid flow simulation is applied to the calculation of high-speed compressible flows of inert and reactive gas mixtures. In the present case, the flowfield is simulated using the 2-D Euler equations, which are discretized in a cell-centered finite volume procedure on unstructured triangular meshes. Interface fluxes are calculated by a Liou flux vector splitting scheme which has been adapted to an unstructured grid context by the authors. Physicochemical properties are functions of the local mixture composition, temperature, and pressure, which are computed using the CHEMKIN-II subroutines. Computational results are presented for the case of premixed hydrogen–air supersonic flow over a 2-D wedge. In such a configuration, combustion may be triggered behind the oblique shock wave and transition to an oblique detonation wave is eventually obtained. It is shown that the solution adaptive procedure implemented is able to correctly define the important wave fronts. A parametric analysis of the influence of the adaptation parameters on the computed solution is performed.

Self‐avoiding walks over adaptive unstructured grids

Self‐avoiding walks over adaptive unstructured grids

Self‐avoiding walks over adaptive unstructured grids

Self‐avoiding walks over adaptive unstructured grids

Self-avoiding walks over adaptive unstructured grids

In this paper, we present self-avoiding walks as a novel technique to “linearize” a triangular mesh. Unlike space-filling curves which are based on a geometric embedding, our algorithm is combinatorial since it uses the mesh connectivity only. We also show how the concept can be easily modified for adaptive grids that are generated in a hierarchical manner based on a set of simple rules, and made amenable for efficient parallelization. The proposed approach should be very useful in the run-time partitioning and load balancing of adaptive unstructured grids.

710 解適合非構造格子による衝撃波の数値シミュレーション(O.S.7-3 高速/高温現象と可視化3)(オーガナイズドセッション7 : 高速/高温現象と可視化)

710 解適合非構造格子による衝撃波の数値シミュレーション(O.S.7-3 高速/高温現象と可視化3)(オーガナイズドセッション7 : 高速/高温現象と可視化)

Unstructured adaptive grid and grid-free methods for edge plasma fluid simulations

Fluid modelling of an edge plasma is usually performed using a finite-difference scheme on a fixed structured grid. However, both experimental measurement and numerical simulation show the presence of front-like regions characterized by sharp variations of the main plasma parameters such as temperature and radiation power. This is caused in part (i) by strong nonlinearities in the fluid equation coefficients due to abrupt changes of various plasma reaction rates as a function of temperature and (ii) by high anisotropy of the plasma transport along and across magnetic field lines. Manual mesh adoption is usually applied to allow better resolution of the regions with sharp gradients. However, such an approach is very time-consuming and limited. To overcome this problem, we propose to use adaptive unstructured meshes constructed with a new quasi-one-dimensional adaption algorithm. This approach is fast and conservative because we use a new finite-volume scheme. The price of adaptation is high, because numerical algorithms became much more complicated. To avoid unwanted complexity, we suggest an alternative use of a grid-free method, which requires no connectivity of arbitrarily placed vertices. To benchmark the methods and codes in two dimensions, we find analytical and semi-analytical solutions of the nonlinear diffusion–radiation equation, which may have sharp fronts, unconnected boundaries and bifurcated solutions. We use these solutions to study the efficiency of the proposed numerical algorithms.

Numerical Study of Interaction of a Vortical Density Inhomogeneity with Shock and Expansion Waves

We studied the interaction of a vortical density inhomogeneity (VDI) with shock and expansion waves. We call the VDI the region of concentrated vorticity (vortex) with a density different from that of ambiance. Non-parallel directions of the density gradient normal to the VDI surface and the pressure gradient across a shock wave result in an additional vorticity. The roll-up of the initial round VDI towards a non-symmetrical shape is studied numerically. Numerical modeling of this interaction is performed by a 2-D Euler code. The use of an adaptive unstructured numerical grid makes it possible to obtain high accuracy and capture regions of induced vorticity with a moderate overall number of mesh points. For the validation of the code, the computational results are compared with available experimental results and good agreement is obtained. The interaction of the VDI with a propagating shock wave is studied for a range of initial and induced circulations and obtained flow patterns are presented. The splitting of the VDI develops into the formation of a non-symmetrical vortex pair and not in a set of vortices. A method for the analytical computation of an overall induced circulation T1 as a result of the interaction of a moving VDI with a number of waves is proposed. Simplified, approximated, expressions for it are derived and their accuracy is discussed. The splitting of the VDI passing through the Prandtl-Meyer expansion wave is studied numerically. The obtained VDI patterns are compared to those for the interaction of the VDI with a propagating shock wave for the same values of initial and induced circulations. These patterns have similar shapes for corresponding time moments.

The influence of entrance geometry of circular reflectors on shock wave focusing

The influence of entrance shape bluntness of circular reflectors on the focusing of reflected shock waves was studied numerically and experimentally. The numerical simulation was conducted using a Godunov-type finite-volume scheme on adaptive unstructured grids and the experiment was conducted in a shock tube equipped with a holographic interferometer. The shock wave Mach number was 1.4 in air at atmospheric condition. It is found that, depending on the bluntness of the reflector entrance shape, the peak value of the focusing pressure varies drastically and is strongly influenced by the process of wave interaction during the focusing.

Numerical Simulation of an Intense Shock Wave Implosion In an Axisymmetric Compartment.

A shock wave implosion in an axisymmetric cavity filled in with a perfect gas and confined by plane and spherical surfaces which touch one another at the symmetry axis is analyzed numerically. The numerical approach is based on a locally adaptive unstructured grid technique and high-order accurate Godunov-type non-oscillatory scheme for the Euler equations. The increase in gas density and pressure as the converging shock wave approaches the axis is shown to be more intense than that by cylindrical or spherical shock implosion. A good agreement with analytical predictions and the experiment on hand is achieved.

ADAPTIVE UNSTRUCTURED GRID FOR THREE-DIMENSIONAL INTERFACE REPRESENTATION

Moving-boundary problems arise in numerous important physical phenomena, and often form complex shapes during their evolution. The ability to track the interface in such cases in two dimensions is well established. However, modifying the grid representing the interface as it evolves in three-dimensional space introduces additional issues. In the current work, three-dimensional interfaces are represented by adaptive unstructured grids. The grids are restructured and refined based on the shape and size of the triangular elements in the grid that forms the interfaces. As the interface deforms, points are automatically added to ensure that the accuracy of interface representation remains consistent. Results are presented to show how complex interface features, including surface curvatures and normals, can be captured by modifying an existing method that uses an approximation to the Dupin indicatrix.