Unstructured Mesh Adaptation Research Articles

A novel stabilization method for high-order shock fitting with finite element methods

A moving-grid, shock-fitting, finite element method has been implemented that can achieve high-order accuracy for flow simulations with shocks. In this approach, element edges in the computational mesh are fitted to the shock front and moved with the shock throughout the simulation. The Euler or Navier-Stokes equations are solved on the moving mesh in an arbitrary Lagrangian-Eulerian framework. The method is implemented in two-dimensions in the context of a streamwise upwind Petrov-Galerkin finite element discretization with unstructured triangular meshes and mesh adaptation. It is shown that the shock interface motion equation has a wave nature, and disturbances can propagate along the shock interface. A SUPG stabilization term is introduced to the interface motion equation that is critical for ensuring that interface disturbances do not lead to non-convergent solution behavior. The formal order of accuracy of the scheme is verified, and the performance of the proposed scheme is assessed for both inviscid and viscous problems. It was found that the present scheme predicts smooth and noise-free surface heating for hypersonic flow over a cylinder with purely irregular triangular elements.

An arbitrary Lagrangian-Eulerian RKDG method for multi-material flows on adaptive unstructured meshes

In this paper, we propose an arbitrary Lagrangian Eulerian (ALE) method for solving compressible multi-material flows on two-dimensional adaptive unstructured triangular meshes. We couple a conservative equation related to a γ-model (or a mass fractional model) with the system of fluid equations for obtaining the specific heat ratio of the multi-material flows. The discretization of the coupling system is implemented by Runge-Kutta Discontinuous Galerkin (RKDG) method and the vertex velocity is obtained by the variational approach. The new meshes can be automatically redistributed and concentrated on regions with large gradient values. This work is a new development of our previous research for solving single-material flow with ALE-RKDG method. The proposed method is more concise compared to many other methods and robust for the simulations of multi-material flows. Numerical examples are presented to verify this method, and the results show that our scheme is not only efficient but also with the anticipative accuracy.

A three-phase interpenetrating continua approach for wave and porous structure interaction

PurposeThis paper aims to propose a three-phase interpenetrating continua model for the numerical simulation of water waves and porous structure interaction.Design/methodology/approachIn contrast with one-fluid formulation or multi-component methods, each phase has its own characteristics, density, velocity, etc., and each point is occupied by all phases. First, the porous structure is modelled as a phase of continua with a penalty force adding on the momentum equation, so the conservation of mass is guaranteed without source terms. Second, the adaptive unstructured mesh modelling with P1DG-P1 elements is used here to decrease the total number of degree of freedom maintaining the same order of accuracy.FindingsSeveral benchmark problems are used to validate the model, which includes the Darcy flow, classical collapse of water column and water column with a porous structure. The interpenetrating continua model is a suitable approach for water wave and porous structure interaction problem.Originality/valueThe interpenetrating continua model is first applied for the water wave and porous structure interaction problem. First, the structure is modelled as phase of non-viscous fluid with penalty force, so the break of the porous structure, porosity changes can be easily embedded for further complex studies. Second, the mass conservation of fluids is automatically satisfied without special treatment. Finally, adaptive anisotropic mesh in space is employed to reduce the computational cost.

A new anisotropic adaptive mesh photochemical model for ozone formation in power plant plumes

Abstract In this work, an advanced dynamically adaptive unstructured mesh technique is introduced to photochemical modeling, which provides a consistent way to resolve the complex chemical transport processes over a wide range of spatial scales from meters (near point sources) up to hundred kilometers without the Gaussian distribution assumption (often used in existing subgrid Plume-in-Grid (PinG) models, such as RPM and SCICHEM). To assess the performance of the new photochemical model, the numerical results (NO x and O 3 ) have been compared to the Southern Oxidants Study (SOS) 1999 aircraft plume measurements, where the range of the emission intensity is from 1.8 to 13.9 ton/h. The relative error in the peak value of NO x and O 3 is between 10%–20% within 66 km downwind distance. The results show that the use of dynamically adaptive meshes can reproduce the details of the plume chemistry evolution: the slender puff structure of high NO x concentrations within a few kilometers width near the point sources, and the wing-like structure of ozone concentration during the plume growth, which is hard to capture for the PinG models or photochemical grid models.

Verification of Anisotropic Mesh Adaptation for Turbulent Simulations over ONERA M6 Wing

Unstructured anisotropic mesh adaptation is known to be an efficient way to control discretization errors in computational fluid dynamics simulations. Method verification is required to provide the confidence for routine use in production analysis. The current work aims at verification of anisotropic mesh adaptation for Reynolds-averaged Navier–Stokes simulations over the ONERA M6 wing. The present verification study is performed using four different flow solvers, three different implementations of the metric field, and three mesh mechanics packages. Two of the flow solvers use stabilized finite element discretizations (FUN3D-SFE and general geometry Navier–Stokes), one uses finite volume discretization (FUN3D-FV), and the last one uses mixed finite volume and finite element discretizations (Wolf). The mesh adaptation is based on an error estimator that aims to control the quadratic error term in the linear interpolation of the Mach number. Two sets of adaptations were performed; the first one controls the interpolation error in the norm, and the second one controls the interpolation error in the norm. Convergence studies were performed on the forces and the pitching moment using all four solvers, and the results are compared with previously verified convergence studies on fixed (nonadapted) meshes. Both the forces and pitching moment on adapted meshes are found to be converging to the fine-mesh values faster than those on fixed meshes. In addition to forces and moments, the convergence of surface pressure and skin-friction coefficients at various measurement locations on the wing are also presented. Adapted-mesh surface pressure distributions agree with the fine fixed mesh pressure distributions. Adapted-mesh skin-friction distributions contain high-frequency noise with mean values approaching the fixed mesh pressure skin-friction distributions.

An exactly force-balanced boundary-conforming arbitrary-Lagrangian-Eulerian method for interfacial dynamics

We present an interface conforming method for simulating two-dimensional and axisymmetric multiphase flows. In the proposed method, the interface is composed of straight segments which are part of mesh and move with the flow. This interface representation is an integral part of an Arbitrary Lagrangian-Eulerian (ALE) method on an moving adaptive unstructured mesh. Our principal aim is to develop an accurate and robust computational method for interfacial flows driven by strong surface tension and with weak viscous dissipation. We first construct discrete solutions satisfying the Laplace law on a circular/spherical interfaces exactly, i.e., the balance between the surface tension and the pressure jump across an interface is achieved exactly in a discrete form. The accuracy and stability of these solutions are then investigated for a wide range of Ohnesorge numbers, Oh. The dimensionless amplitude of the spurious current is reduced to machine zero, i.e., on the order of 10−15 for Oh≥10−3. Finally, the accuracy and capability of the proposed method are demonstrated through a series of benchmark tests with larger interface deformations. In particular, the method is validated with Prosperitti's analytic results of the bubble/drop oscillations and Peregrine's dripping faucet experiment, in which the values of Oh are small.

Topography Least-Squares Reverse-Time Migration Based on Adaptive Unstructured Mesh

Least-squares reverse-time migration (LSRTM) attempts to invert the broadband-wavenumber reflectivity image by minimizing the residual between observed and predicted seismograms via linearized inversion. However, rugged topography poses a challenge in front of LSRTM. To tackle this issue, we present an unstructured mesh-based solution to topography LSRTM. As to the forward/adjoint modeling operators in LSRTM, we take a so-called unstructured mesh-based “Grid Method.” Before solving the two-way wave equation with the Grid Method, we prepare for it a velocity-adaptive unstructured mesh using a Delaunay Triangulation plus Centroidal Voronoi Tessellation algorithm. The rugged topography acts as constraint boundaries during mesh generation. Then, by using the adjoint method, we put the observed seismograms to the receivers on the topography for backward propagation to produce the gradient through the cross-correlation imaging condition. We seek the inverted image using the conjugate gradient method during linearized inversion to linearly reduce the data misfit function. Through the 2D SEG Foothill synthetic dataset, we see that our method can handle the LSRTM from rugged topography.

A finite element solver for hypersonic flows in thermo-chemical non-equilibrium, Part II

Purpose This work aims to describe the physical and numerical modeling of a CFD solver for hypersonic flows in thermo-chemical non-equilibrium. This paper is the second of a two-part series that concerns the application of the solver introduced in Part I to adaptive unstructured meshes. Design/methodology/approach The governing equations are discretized with an edge-based stabilized finite element method (FEM). Chemical non-equilibrium is simulated using a laminar finite-rate kinetics, while a two-temperature model is used to account for thermodynamic non-equilibrium. The equations for total quantities, species and vibrational-electronic energy conservation are loosely coupled to provide flexibility and ease of implementation. To accurately perform simulations on unstructured meshes, the non-equilibrium flow solver is coupled with an edge-based anisotropic mesh optimizer driven by the solution Hessian to carry out mesh refinement, coarsening, edge swapping and node movement. Findings The paper shows, through comparisons with experimental and other numerical results, how FEM + anisotropic mesh optimization are the natural choice to accurately simulate hypersonic non-equilibrium flows on unstructured meshes. Three-dimensional test cases demonstrate how, for high-speed flows, shocks resolution, and not necessarily boundary layers resolution, is the main driver of solution accuracy at walls. Equally distributing the error among all elements in a suitably defined Riemannian space yields highly anisotropic grids that feature well-resolved shock waves. The resulting high level of accuracy in the computation of the enthalpy jump translates into accurate wall heat flux predictions. At the opposite end, in all cases examined, high-quality but isotropic unstructured meshes gave very poor solutions with severely inadequate heat flux distributions not even featuring expected symmetries. The paper unequivocally demonstrates that unstructured anisotropically adapted meshes are the best, and may be the only, way for accurate and cost-effective hypersonic flow solutions. Originality/value Although many hypersonic flow solvers are developed for unstructured meshes, few numerical simulations on unstructured meshes are presented in the literature. This work demonstrates that the proposed approach can be used successfully for hypersonic flows on unstructured meshes.

A front tracking method for simulation of two-phase interfacial flows on adaptive unstructured meshes for complex geometries

A novel numerical algorithm and modeling framework of a front tracking method based on adaptive anisotropic unstructured meshes for simulating two-phase interfacial flows is presented. In the traditional front tracking methods, a fixed uniform Eulerian Cartesian mesh is used for solving the fluid flow, and adaptive unstructured grid markers are used for tracking the phase-interface front. In the new algorithm, an adaptive anisotropic unstructured mesh is used for solving the fluid flow, as well as for tracking the phase-interface front. Special attentions are focused on developing an algorithm for physical variable interpolation between the two sets of unstructured meshes for both the fluid flow and the front movement. A modeling framework for the described numerical algorithm is implemented on the platform of the commercial CFD package ANSYS Fluent through user-defined functions. The advanced ANSYS Fluent fluid flow solver feature of using adaptive unstructured mesh is integrated with the front tracking method, which can handle complex boundary geometries and has high numerical efficiency. These advanced features are demonstrated through three numerical test examples of simulating a single gas bubble rising freely in a viscous liquid, a buoyancy-driven liquid droplet rising in a periodically constricted capillary tube, and a pressure-driven droplet passing through a small throat hole in a pipe. The accuracy of the simulation results is demonstrated through the comparison with those observed in experiments or obtained using other simulation methods.

A high‐order Runge‐Kutta discontinuous Galerkin method with a subcell limiter on adaptive unstructured grids for two‐dimensional compressible inviscid flows

SummaryA robust, adaptive unstructured mesh refinement strategy for high‐order Runge‐Kutta discontinuous Galerkin method is proposed. The present work mainly focuses on accurate capturing of sharp gradient flow features like strong shocks in the simulations of two‐dimensional inviscid compressible flows. A posteriori finite volume subcell limiter is employed in the shock‐affected cells to control numerical spurious oscillations. An efficient cell‐by‐cell adaptive mesh refinement is implemented to increase the resolution of our simulations. This strategy enables to capture strong shocks without much numerical dissipation. A wide range of challenging test cases is considered to demonstrate the efficiency of the present adaptive numerical strategy for solving inviscid compressible flow problems having strong shocks.

Multi-scale thermal response modeling of an AVCOAT-like thermal protection material

A multi-scale modeling approach based on the stochastic Direct Simulation Monte Carlo (DSMC) and walker methods is developed to understand the complex flows and thermophysical phenomena through a syntactic foam TPS, similar to AVCOAT. Using novel, unstructured adaptive mesh refinement/Octree grids and newly developed subsonic boundary conditions, the counter-flow transport of boundary layer and pyrolysis gases through the porous microstructure is modeled for the first time. Permeability of the microstructure models having porosities of 0.71 and 0.86 is computed in the DSMC simulations and compared to a fibrous TPS material. The rigorous development of a stochastic based thermal response model that can couple convective, conductive, and radiative heat transfer through a porous material having non-uniform thermophysical properties and high temperature gradients is presented and compared with a one-dimensional finite-volume approach. The material thermal response is found to be dominated by conduction, yet, the interactions between boundary layer and pyrolysis species on the actual 3-D geometry, which cannot be considered in traditional material response solvers, may in fact cause them to underpredict the TPS material temperature.

An Improved Algorithm for Drift Diffusion Transport and Its Application on Large Scale Parallel Simulation of Resistive Random Access Memory Arrays

A hybrid finite volume–finite element method which can avoid overestimation of volume shared by each vertex in the meshing grid is proposed to solve the diffusive transport governed continuity equation. The simulation results demonstrate that the improved algorithm can eliminate unphysical distortions as compared to the conventional Scharfetter Gummel method. Based on the proposed algorithm, a parallel-computation simulator is developed for large-scale electrothermal simulation of resistive random access memory (RRAM) arrays, in which the domain decomposition method and J parallel adaptive unstructured mesh applications infrastructure are adopted. The validity, speedup, and scalability of the parallel simulator are investigated on the TianHe-2 supercomputer. Based on the simulated results, the electrothermal characteristics and reliability analysis of large-scale RRAM arrays are investigated in detail.

Simulating Aerodynanics of a Moving Body Specified by Immersed Boundaries on Dynamically Adaptive Unstructured Meshes

An integrated technology is developed for the numerical simulation of the aerodynamics of moving bodies described by the immersed body method on unstructured meshes. The calculation accuracy is enhanced by the dynamic adaptation of the meshes. The method of grid adaptation is based on the technique of the redistribution of nodes implemented through solving an additional differential equation of the grid motion. This method enables retaining the original grid topology and does not incur a significant increase in computational costs. The technology is developed for 2D formulations and verified on model problems.

Modelling of fluid-structure interaction for moderate reynolds number flows using an immersed-body method

An unsteady Reynolds-averaged Navier–Stokes (URANS) model coupled with an immersed-body method is used to model fluid-structure interaction (FSI) for moderate Reynolds number flows. Particular attention is paid to the application of suitable flow boundary conditions with the immersed-body method. This model couples a combined finite-discrete element solid model and a finite element fluid model with the standard k−ε model. A thin shell mesh surrounding the solid surface is first used as a delta function to apply the interface boundary conditions for both the URANS model and the momentum equation. In order to reduce the computational cost, a log-law wall function is used within this thin shell to resolve the flow near the solid wall. To improve the accuracy of the wall function, a novel shell mesh external-surface intersection approach is introduced to identify sharp solid-fluid interfaces. More importantly, an unstructured anisotropic mesh adaptivity is used to refine the mesh according to the interface and the velocity, which improves the accuracy of this immersed-body URANS model with use of a limited number of fluid cells. This immersed-body URANS method is validated by several test cases and results are in good agreement with both experimental and numerical data from the literature.

Numerical simulation of floods from multiple sources using an adaptive anisotropic unstructured mesh method

The coincidence of two or more extreme events (precipitation and storm surge, for example) may lead to severe floods in coastal cities. It is important to develop powerful numerical tools for improved flooding predictions (especially over a wide range of spatial scales - metres to many kilometres) and assessment of joint influence of extreme events. Various numerical models have been developed to perform high-resolution flood simulations in urban areas. However, the use of high-resolution meshes across the whole computational domain may lead to a high computational burden. More recently, an adaptive isotropic unstructured mesh technique has been first introduced to urban flooding simulations and applied to a simple flooding event observed as a result of flow exceeding the capacity of the culvert during the period of prolonged or heavy rainfall. Over existing adaptive mesh refinement methods (AMR, locally nested static mesh methods), this adaptive unstructured mesh technique can dynamically modify (both, coarsening and refining the mesh) and adapt the mesh to achieve a desired precision, thus better capturing transient and complex flow dynamics as the flow evolves.In this work, the above adaptive mesh flooding model based on 2D shallow water equations (named as Floodity) has been further developed by introducing (1) an anisotropic dynamic mesh optimization technique (anisotropic-DMO); (2) multiple flooding sources (extreme rainfall and sea-level events); and (3) a unique combination of anisotropic-DMO and high-resolution Digital Terrain Model (DTM) data. It has been applied to a densely urbanized area within Greve, Denmark. Results from MIKE 21 FM are utilized to validate our model. To assess uncertainties in model predictions, sensitivity of flooding results to extreme sea levels, rainfall and mesh resolution has been undertaken. The use of anisotropic-DMO enables us to capture high resolution topographic features (buildings, rivers and streets) only where and when is needed, thus providing improved accurate flooding prediction while reducing the computational cost. It also allows us to better capture the evolving flow features (wetting-drying fronts).

Performance of Adaptive Unstructured Mesh Modelling in Idealized Advection Cases over Steep Terrains

Advection errors are common in basic terrain-following (TF) coordinates. Numerous methods, including the hybrid TF coordinate and smoothing vertical layers, have been proposed to reduce the advection errors. Advection errors are affected by the directions of velocity fields and the complexity of the terrain. In this study, an unstructured adaptive mesh together with the discontinuous Galerkin finite element method is employed to reduce advection errors over steep terrains. To test the capability of adaptive meshes, five two-dimensional (2D) idealized tests are conducted. Then, the results of adaptive meshes are compared with those of cut-cell and TF meshes. The results show that using adaptive meshes reduces the advection errors by one to two orders of magnitude compared to the cut-cell and TF meshes regardless of variations in velocity directions or terrain complexity. Furthermore, adaptive meshes can reduce the advection errors when the tracer moves tangentially along the terrain surface and allows the terrain to be represented without incurring in severe dispersion. Finally, the computational cost is analyzed. To achieve a given tagging criterion level, the adaptive mesh requires fewer nodes, smaller minimum mesh sizes, less runtime and lower proportion between the node numbers used for resolving the tracer and each wavelength than cut-cell and TF meshes, thus reducing the computational costs.

In‐memory integration of existing software components for parallel adaptive unstructured mesh workflows

SummaryReliable mesh‐based simulations are needed to solve complex engineering problems. Mesh adaptivity can increase reliability by reducing discretization errors but requires multiple software components to exchange information. Often, components exchange information by reading and writing a common file format. This file‐based approach becomes a problem on massively parallel computers where filesystem bandwidth is a critical performance bottleneck. Our approach using data streams and component interfaces avoids the filesystem bottleneck. In this paper, we present these techniques and their use for coupling mesh adaptivity to the PHASTA computational fluid dynamics solver, the Albany multi‐physics framework, and the Omega3P linear accelerator frequency analysis applications. Performance results are reported on up to 16,384 cores of an Intel Knights Landing‐based system.

Unstructured mesh adaptivity for urban flooding modelling

Over the past few decades, urban floods have been gaining more attention due to their increase in frequency. To provide reliable flooding predictions in urban areas, various numerical models have been developed to perform high-resolution flood simulations. However, the use of high-resolution meshes across the whole computational domain causes a high computational burden. In this paper, a 2D control-volume and finite-element flood model using adaptive unstructured mesh technology has been developed. This adaptive unstructured mesh technique enables meshes to be adapted optimally in time and space in response to the evolving flow features, thus providing sufficient mesh resolution where and when it is required. It has the advantage of capturing the details of local flows and wetting and drying front while reducing the computational cost. Complex topographic features are represented accurately during the flooding process. For example, the high-resolution meshes around the buildings and steep regions are placed when the flooding water reaches these regions.In this work a flooding event that happened in 2002 in Glasgow, Scotland, United Kingdom has been simulated to demonstrate the capability of the adaptive unstructured mesh flooding model. The simulations have been performed using both fixed and adaptive unstructured meshes, and then results have been compared with those published 2D and 3D results. The presented method shows that the 2D adaptive mesh model provides accurate results while having a low computational cost.

Sprai: coupling of radiative feedback and primordial chemistry in moving mesh hydrodynamics

In this paper we introduce a new radiative transfer code SPRAI (Simplex Photon Radiation in the Arepo Implementation) based on the SimpleX radiation transfer method. This method, originally used only for post-processing, is now directly integrated into the Arepo code and takes advantage of its adaptive unstructured mesh. Radiated photons are transferred from the sources through the series of Voronoi gas cells within a specific solid angle. From the photon attenuation we derive corresponding photon fluxes and ionization rates and feed them to a primordial chemistry module. This gives us a self-consistent method for studying dynamical and chemical processes caused by ionizing sources in primordial gas. Since the computational cost of the SimpleX method does not scale directly with the number of sources, it is convenient for studying systems such as primordial star-forming halos that may form multiple ionizing sources.

Massively Parallel Simulation of Large-Scale Electromagnetic Problems Using One High-Performance Computing Scheme and Domain Decomposition Method

Massively parallel simulation of large-scale electromagnetic problems is performed on a supercomputer using an in-house developed high-performance computing scheme together with a domain decomposition method, where parallel adaptive unstructured mesh generation is at first performed for modeling an arbitrary multiscale structure. The accuracy, speedup, as well as scalability of such parallel scheme are numerically tested and validated during its implementation for simulating electromagnetic environmental effects (E3) on a ship platform using the TianHe-II supercomputer. It is demonstrated that this method can overcome the convergence deficiency of conventional iterative solver. In addition, numerical experiments are also carried out to show its adaptability to the number of subdomains and object electrical size. It is believed that our developed solver can be further used for solving various E3 or electromagnetic compatibility problems for the design of many large-scale platforms.