Unstructured Mesh Adaptation Research Articles

Stress-Equivalent Spalart–Allmaras Wall Model with Local Boundary Conditions for Reynolds-Averaged Navier–Stokes

In this paper, we present a wall model based on a modified version of the Spalart–Allmaras turbulence model. Unlike typical wall models, this method avoids the need to query the interior solution by utilizing solution information solely at the boundary, making it well-suited for unstructured grids and mesh adaptation. Furthermore, this wall-modeling method is formulated to lessen the near-wall grid resolution requirements by, below the log layer, making the eddy viscosity approach a constant, nonzero value and the velocity varying approximately linearly with distance from the wall. Using output-based mesh adaptation, this new wall-modeling method is compared to standard Reynolds-Averaged Navier-Stokes (RANS-SA). It is shown that this wall model results in accurate predictions of quantities of interest such as aerodynamic coefficients, surface pressure and temperature, skin friction, and heat transfer compared with RANS-SA, while requiring substantially less near-wall grid.

Joint inversion of potential field data with adaptive unstructured tetrahedral mesh

Inverting potential field data presents a significant challenge due to its ill-posed nature, often leading to nonunique model solutions. Addressing this, our work focuses on developing a robust joint inversion method for potential field data, aiming to achieve more accurate density and magnetic susceptibility distributions. Unlike most previous work that used regular meshes, our approach adopts an adaptive, unstructured tetrahedral mesh, offering enhanced capabilities in handling the inverse problem of potential field methods. During inversion, the tetrahedral mesh is refined in response to the model update rate. We integrate a Gramian constraint into the objective function, allowing the enforcement of model similarity in terms of either the model parameters or their spatial gradients on an unstructured mesh. In addition, we use the moving least-squares method for gradient operator computation, which is essential for model regularization. Our model studies indicate that this method effectively inverts potential field data, yielding reliable subsurface density and magnetic susceptibility distributions. The joint inversion approach, compared with individual data set inversion, produces coherent geophysical models with enhanced correlations. Notably, it significantly mitigates the nonuniqueness problem, with the recovered anomaly locations aligning more closely with actual ground truths. Applying our methodology and algorithm to field data from the Ring of Fire area in Canada, the joint inversion process has generated comprehensive geophysical models with robust correlations, offering potential benefits for mineral exploration in the region.

Predicting lift and drag coefficients during hypersonic Mars reentry using hyStrath

During hypersonic reentry, a spacecraft experiences several different fluid flow regimes, which usually require the application of different software frameworks to simulate the respective regimes. This study aims to evaluate the hyStrath library for predicting aerodynamic lift and drag coefficients of complex three-dimensional (3D) geometries during hypersonic Mars reentry, using flight data of the Viking 1 mission as reference. A range of altitudes (h=30−140 km) and Mach numbers (M=13−24) where flight data is available is considered, covering the rarefied, transitional, and continuum fluid flow regimes. The hyStrath library contains a set of modified solvers and state-of-the-art thermophysical and chemistry models within the framework of OpenFOAM, dedicated to modeling high-enthalpy hypersonic flow problems. Depending on the flow regime, the computational fluid dynamics solver hy2Foam or direct-simulation Monte Carlo solver dsmcFoam+ are employed in the study. Because hyStrath is based on OpenFOAM, it allows the use of an unstructured adaptive mesh refinement approach for arbitrary geometries. We obtain excellent results throughout all investigated flow regimes and Mach numbers with an average deviation of 1.5% and 2% from the measured lift and drag coefficients, respectively. The applicability of the framework for accurately modeling both rarefied and continuum Mars reentry problems of complex 3D geometries such as the Viking capsule is demonstrated.

An implicit-in-time DPG formulation of the 1D1V Vlasov-Poisson equations

Efficient solution of the Vlasov equation, which can be up to six-dimensional, is key to the simulation of many difficult problems in plasma physics. The discontinuous Petrov-Galerkin (DPG) finite element methodology provides a framework for the development of stable (in the sense of Ladyzhenskaya–Babuška–Brezzi conditions) finite element formulations, with built-in mechanisms for adaptivity. While DPG has been studied extensively in the context of steady-state problems and to a lesser extent with space-time discretizations of transient problems, relatively little attention has been paid to time-marching approaches. In the present work, we study a first application of time-marching DPG to the Vlasov equation, using backward Euler for a Vlasov-Poisson discretization. We demonstrate adaptive mesh refinement for two problems: the two-stream instability problem, and a cold diode problem. We believe the present work is novel both in its application of unstructured adaptive mesh refinement (as opposed to block-structured adaptivity, which has been studied previously) in the context of Vlasov-Poisson, as well as in its application of DPG to the Vlasov-Poisson system. We also discuss extensive additions to the Camellia library in support of both the present formulation as well as extensions to higher dimensions, Maxwell equations, and space-time formulations.

Experience in Numerical Hydrodynamic Simulation of Long River Reaches

The article formulates the main requirements to numerical algorithms for hydrodynamic 2D-modeling of long and very long river segments with lengths of up to several thousand kilometers. The main feature is the use of adaptive unstructured mesh along with algorithms that give correct values of water surface elevations on coarse mesh, taking into account abrupt changes of bed elevations. A hydrodynamic model of a segment of the Amur R. with a total length of 3 thous. km is presented, which is based on a numerical solution of two-dimensional shallow-water equations (Saint-Venant) by a new high-accuracy algorithm, taking into account road and protection structures in the floodplain. The stages of model construction and verification are described, and the results of calculations for an extraordinary flood in 2013 and a high flood in 2020 are given. Water levels (with estimates of their errors) and the rates of water discharge at gages are given along with flow fields and the inundation zones of floodplain areas.

Isotropic and anisotropic mesh adaptation for RANS simulations of a nacelle under crosswind conditions

Mesh adaptation of unstructured meshes for aerodynamic simulations, that typically resolve the Reynolds Averaged Navier-Stokes (RANS) equations, is a promising approach to enable high numerical precision on complex geometries. Its objective is to minimize the discretization error without using empirical meshing guidelines. The most common approach of mesh adaptation is the “feature-based” isotropic mesh adaptation: from an initial flow prediction on an isotropic unstructured mesh, a local error estimator is computed using a flow variable. It is then used to adapt the mesh using isotropic tetrahedra. Additional near-wall resolution can be achieved by extruding prism layers from the walls. A more efficient approach is to use anisotropic mesh adaptation purely with tetrahedra that are stretched to follow the flow's preferential directions. In this work, we demonstrate the abilities of feature-based isotropic and anisotropic mesh adaptation on a complex flow phenomenon of importance for jet engines: flow separation in a nacelle under crosswind conditions. Two different solvers, adapted for either isotropic or anisotropic meshes, are employed. Results are compared with standard unstructured simulations with user-imposed mesh refinements and highlight the ability of mesh adaptation to automatically capture all the relevant flow phenomena without any user input and at reduced mesh size.

МЕЛКОМАСШТАБНОЕ МОДЕЛИРОВАНИЕ ДИНАМИКИ ВОД НА ШЕЛЬФЕ И КОНТИНЕНТАЛЬНОМ СКЛОНЕ В АНТАРКТИКЕ

The use of the Fluidity-ICOM model in a full non-hydrostatic formulation makes it possible to correctly investigate fine-scale water dynamics and water transformations on the Antarctic shelf and continental slope. A possibility of solving problems with high spatial resolution in models is provided by the use of the three-dimensional adaptive unstructured mesh with automatic refinement to given scales. The modernization of the graphical model output made it possible to reliably visualize the detailed development of simulated hydrophysical processes, to obtain numerical estimates of parameters of these processes, and to verify them against unique field observation data. An original three-dimensional numerical experiment was held in the area of polynya with an open water surface on the shelf. In this case, the real salt (buoyancy) flux is specified, which is caused by the in-water ice formation in the polynya and is obtained from the actual atmospheric forcing. As a result, the convective circulation was correctly simulated as a process of formation of dense water on the shelf, which then flows down the shelf and continental slope in the form of discrete density currents. Similarity of the model geometric, dynamic, and hydrophysical characteristics of cascading with the typical ones obtained from the analysis of field observations was found.

Anisotropic mesh generation and adaptation for quads using the Lp-CVT method

This paper presents a framework for anisotropic unstructured all-quad mesh adaptation. The technique is suitable for use with a diverse class of numerical methods, including the high-order Discontinuous Galerkin solver presented here. Benefiting from the flexibility and efficiency of these methods, improvements in the solution accuracy are targeted by modifying the discretization of the domain. Previous works have tackled this problem for the case of simplex elements using continuous mesh and error models. Our method makes use of novel extensions to allow similar techniques to be applied for the case of tensor product elements. Key aspects of the work will discuss the modified continuous mesh representation and error minimization procedure. Additionally, these ideas have been coupled with mesh generation based on both existing and experimental techniques. As a result, this work will also consider the implementation of an energy minimizing, node redistribution method, that takes place in an anisotropic spatially varying high-order p-norm. Finally, the technique will also be applied to goal-oriented adaption using the adjoint-based error estimation. Overall, the work outlines the adaptive procedure tailored specially to all-quad meshing.

Topology optimization for lift–drag problems incorporated with distributed unstructured mesh adaptation

Topology optimization for lift–drag problems incorporated with distributed unstructured mesh adaptation

An unstructured adaptive mesh refinement approach for computational fluid dynamics of reacting flows

A new Direct Numerical Simulation (DNS) code HAMISH with Adaptive Mesh Refinement (AMR) has been developed to simulate compressible reacting flow in a computationally economical manner. The focus is on problems where high gradients of temperature, density and species mass fraction remain localised, for example within the interior structure of flames. The resolution requirements of such local high-gradient regions often determine the global mesh spacing when uniform meshes are used. The numerical framework in HAMISH is based on an unstructured finite-volume approach together with a Runge-Kutta algorithm for time-stepping. The unstructured Cartesian mesh used in HAMISH allows for adaptive refinement and de-refinement of the local mesh depending on the demands of the flow physics and numerical accuracy. The code utilises an octree data structure and a Morton space-filling curve, allowing efficient cell division as well as straightforward parallel domain decomposition. The spatial discretisation scheme uses fourth-order polynomial reconstruction to evaluate the inter-cell fluxes. A third-order three-step explicit Runge-Kutta time-marching algorithm is used together with adaptive time-stepping with proportional-integral-type error control using an embedded Runge-Kutta scheme. The code is fully parallelised through domain decomposition over an arbitrary number of processors and exhibits a high level of parallel efficiency. In this paper the key capabilities of HAMISH are demonstrated based on a number of test cases. These test cases include (a) simulation of 1-D planar laminar premixed flames to demonstrate the capability of AMR in capturing the sharp gradients within the flame; (b) fully developed laminar channel flow, which shows that the code is capable of refining the mesh in the boundary layer next to the wall; (c) 2-D expanding flame under quiescent laminar condition, which demonstrates that the code is capable of dynamic local mesh refinement based on the position of the flame front; (d) 3-D non-reacting Taylor-Green vortex which demonstrates HAMISH can deal with vortical motion typical of turbulent flows; (e) 3-D premixed turbulent flame propagation under isotropic homogeneous decaying turbulence to demonstrate that the code can be employed for production level DNS of turbulent reacting flows.

Nonlinear Finite Volume Method for the Interface Advection-Compression Problem on Unstructured Adaptive Meshes

Nonlinear Finite Volume Method for the Interface Advection-Compression Problem on Unstructured Adaptive Meshes

A novel dynamic adaptive unstructured mesh algorithm for simulating multi‐object relative motion in incompressible fluid

AbstractA novel dynamic adaptive unstructured mesh (DAUM) algorithm is proposed to solve incompressible multi‐object relative motion (MORM). The DAUM algorithm, consisting of exponential function deformation, adaptive edge swapping, and area Laplace smoothing, can greatly improve dynamic mesh robustness and perfectly overcome mesh skewness. The core of DAUM is the adaptive edge swapping inspired by Delaunay triangulation, which is distinguished from traditional edge swapping. The adaptive edge swapping can fully consider the relationship of neighbor elements only using Delaunay triangulation. Meanwhile, the implementation and reliability of adaptive edge swapping are better than the traditional edge swapping method due to eliminating the interference of the non‐convex polygon, so more code remedies can be avoided. Using the DAUM, none of the vertices is inserted or deleted so that the manipulation of the dynamic mesh is easily implemented and maintains computational efficiency in the process of mesh motion. Three representative geometries are used to assess the performance of the DAUM in MORM. To systematically analyze the advantages of DAUM, two relatively moving cylinders have been numerically investigated in incompressible flow. The inline force and lift force profiles on two cylinders are obtained and analyzed by using the flow field information. Three interaction stages are divided based on the parameter G and the interactional intensity of two inner anticlockwise vortices is considered as the division criteria. At the running process of the DAUM algorithm, the dynamic mesh quality is well controlled and remains in the high‐quality range based on the aspect ratio (AR) criterion. The results indicate that the proposed DAUM algorithm can properly solve the difficulties caused by MORM, especially for period oscillation motion.

Simulation of the Flow near a Rotating Propeller on Adaptive Unstructured Meshes Using the Immersed Boundary Method

Simulation of the Flow near a Rotating Propeller on Adaptive Unstructured Meshes Using the Immersed Boundary Method

High-performance 3D Unstructured Mesh Deformation Using Rank Structured Matrix Computations

The Radial Basis Function (RBF) technique is an interpolation method that produces high-quality unstructured adaptive meshes. However, the RBF-based boundary problem necessitates solving a large dense linear system with cubic arithmetic complexity that is computationally expensive and prohibitive in terms of memory footprint. In this article, we accelerate the computations of 3D unstructured mesh deformation based on RBF interpolations by exploiting the rank structured property of the matrix operator. The main idea consists in approximating the matrix off-diagonal tiles up to an application-dependent accuracy threshold. We highlight the robustness of our multiscale solver by assessing its numerical accuracy using realistic 3D geometries. In particular, we model the 3D mesh deformation on a population of the novel coronaviruses. We report and compare performance results on various parallel systems against existing state-of-the-art matrix solvers.

Parallel CFD-Algorithm on Unstructured Adaptive Meshes

Parallel CFD-Algorithm on Unstructured Adaptive Meshes

High-Efficiency Gravity Data Inversion Method Based on Locally Adaptive Unstructured Meshing

In the 3-D density inversion calculation of gravity data, the entire subsurface space is discretized into rectangular prisms, and the density value of each prism is calculated. However, the method of dividing the entire space often results in invalid calculations. In this study, we proposed a highly efficient density inversion method using a locally adaptive unstructured mesh. In this method, the inversion scope is reduced by using the feature that the zero value of the tilt angle method corresponds to the edge of the field source. In addition, the local inversion area is divided by unstructured meshes, which can better represent irregular geological bodies and undulating terrain. In the proposed method, the size of the grid cells is changed according to the value of the tilt angle to reduce the amount of mesh, which reduces the computational complexity and improves the computational efficiency. In addition, by introducing a volume weighting function, the sensitivity of grid cells of different sizes can be balanced. Through synthetic modeling experiments, we verified that the locally adaptive unstructured mesh method can improve the efficiency and accuracy of inversion, flexibly deal with undulating terrain, and obtain the distribution features of irregular bodies. We applied this method to gravimetric data of the North Qinling region of the Shaanxi province, which clearly shows the spatial distribution information of five high-density geological bodies, and the depth range of ore bodies formed is from 240 to 1481 m according to our inversion results.

Periodic adjoints and anisotropic mesh adaptation in rotating frame for high-fidelity RANS turbomachinery applications

The scope of this paper is to demonstrate the viability and efficiency of metric-based unstructured anisotropic mesh adaptation techniques to turbomachinery applications. The main difficulty in turbomachinery is the periodicity of the domain that must be taken into account in the mesh-adaptive solution process. The periodicity is strongly enforced in the flow solver using ghost entities to minimize the impact on the source code. For the mesh adaptation, the local remeshing is done in two steps. First, the inner domain is remeshed with frozen periodic frontiers, and, second, the periodic surfaces are remeshed after moving geometric entities from one side of the domain to the other. One of the main goal of this work is to demonstrate that mesh-independent certified numerical solutions can be obtained thanks to anisotropic mesh adaptation and that it is possible to run high-fidelity CFD on unstructured adapted meshes composed only of tetrahedra. This paper demonstrates how mesh adaptation, thanks to its automation, is able to generate meshes that are extremely difficult to envision and almost impossible to generate manually, leading to highly accurate numerical solutions. This study considers feature-based error estimate based on the standard multi-scale Lp interpolation error estimate and goal-oriented error estimate using an adjoint state to control the error on turbomachinery output functionals. A description of the flow solver and the adjoint solver is given in this work, as they are very different from what is encountered in the turbomachinery community. We also present all the specific modifications that have been introduced in the adaptive process to deal with periodic simulations used for turbomachinery applications. The periodic mesh adaptation strategy is then tested and validated on the LS89 high pressure axial turbine vane and the NASA Rotor 37 test cases.

Comparing Unstructured Adaptive Mesh Solutions for the High Lift Common Research Airfoil

Discretization error is a common source of uncertainty in computational fluid dynamics (CFD) analyses. Traditional means of controlling discretization error through fixed-mesh refinement studies have proved to be difficult particularly when modeling complex geometries and flowfields. One reason for this is that mesh generation in today’s production CFD workflow is often a labor-intensive process that is heavily dependent on user judgment. Unstructured mesh adaptation is known to be an efficient way to control discretization errors in CFD. Adaptive methods replace user-based decision-making with automated processes that optimize a mesh to reduce discretization error. This paper compares the application of multiple solution adaptive techniques in combination with multiple flow solvers to solve for the flowfield about a 2-D airfoil section of the NASA High-Lift Common Research Model. By driving the adaptive mesh processes to a similar level of mesh convergence, the ability to achieve consistent results between multiple adaptive techniques and flow solvers is demonstrated. Mesh convergence for the various adaptive mesh approaches is compared, identifying potential areas for improvement and providing mesh generation guidance for future workshops.

Efficient exascale discretizations: High-order finite element methods

Efficient exploitation of exascale architectures requires rethinking of the numerical algorithms used in many large-scale applications. These architectures favor algorithms that expose ultra fine-grain parallelism and maximize the ratio of floating point operations to energy intensive data movement. One of the few viable approaches to achieve high efficiency in the area of PDE discretizations on unstructured grids is to use matrix-free/partially assembled high-order finite element methods, since these methods can increase the accuracy and/or lower the computational time due to reduced data motion. In this paper we provide an overview of the research and development activities in the Center for Efficient Exascale Discretizations (CEED), a co-design center in the Exascale Computing Project that is focused on the development of next-generation discretization software and algorithms to enable a wide range of finite element applications to run efficiently on future hardware. CEED is a research partnership involving more than 30 computational scientists from two US national labs and five universities, including members of the Nek5000, MFEM, MAGMA and PETSc projects. We discuss the CEED co-design activities based on targeted benchmarks, miniapps and discretization libraries and our work on performance optimizations for large-scale GPU architectures. We also provide a broad overview of research and development activities in areas such as unstructured adaptive mesh refinement algorithms, matrix-free linear solvers, high-order data visualization, and list examples of collaborations with several ECP and external applications.

Feature-based and goal-oriented anisotropic mesh adaptation for RANS applications in aeronautics and aerospace

The scope of this paper is to demonstrate the viability of unstructured anisotropic mesh adaptation for commercial aircraft drag and high-lift prediction studies. The main achievement of this work is to demonstrate that mesh-independent certified numerical solutions can be achievable thanks to anisotropic mesh adaptation and that it is possible to run high-fidelity CFD on unstructured adapted meshes composed only of tetrahedra which is fundamental to design robust meshing process for complex geometries. It also points out the early capturing property of the solution-adaptive process in the sense that accurate output functional values are obtained on relatively coarse adapted meshes. On a more practical point of view, this paper demonstrates how mesh adaptation, thanks to its automation, is able to generate meshes that are extremely difficult to envision and almost impossible to generate manually, leading to highly accurate numerical solutions. Moreover, as the process can start from any coarse initial mesh, it greatly simplifies the overall meshing process. This study also analyze the influence of different strategies in the mesh adaptation algorithm and in the error analysis which are key components of the process. Several error estimates are considered: feature-based ones which are based on the standard multiscale Lp interpolation error estimate and goal-oriented ones to control the error on output functionals which rely on an accurate computation of the adjoint state. The adjoint problem proves to be a stiff problem for RANS equations, failing to converge the adjoint state to machine zero may impact negatively the adaptive process. The maturity of the solution-adaptive process is demonstrated on numerous drag and high-lift prediction cases. It has also excelled in sonic boom and turbomachine applications.