Unstructured Mesh Method Research Articles

Accuracy verification of fast adaptive galerkin finite volume solver for thermal and mechanical load crack propagation in triangular meshes

This study presents the details of the Galerkin finite volume method for triangular unstructured meshes and its application for the fracture analysis of 2D elasticity problems under simultaneous thermal and mechanical loading. The heat diffusion and elasticity equations are discretized using the Galerkin finite volume method (which, due to omitting matrix manipulation calculations, computations are considerably faster than FEM and XFEM Solvers). The maximum tangential stress criterion is presented after briefly describing the interaction integral formulation used to calculate the stress intensity factors in thermo-mechanical problems. The accuracy of the computed results of the present strategy under thermo-mechanical loads is demonstrated using some benchmark test cases. First, a thermal stress analysis of a plate with an inclined central crack under thermal boundary conditions is performed. Second, the development of a crack under mechanical stress boundary conditions is modeled. Third, crack propagation under both thermal and mechanical boundary conditions is simulated. The present modeling strategy's results are compared with those reported in previous numerical works to verify the accuracy. The stress intensity factors and predicted crack trajectories are utilized to assess the accuracy of computed results and investigate the quality of crack simulation by the proposed numerical method.

A cache-efficient reordering method for unstructured meshes with applications to wall-resolved large-eddy simulations

Unstructured meshes provide a distinct advantage for handing complex geometries. However, the low cache utilization due to mesh-related data access patterns raises particular challenges in achieving a high computing efficiency for large-eddy simulations. We propose a geometrical-based mesh reordering method to improve cache utilization. The proposed method utilizes a Hilbert space-filling curve that passes through each cell once, guiding the reordering of the cells of the unstructured mesh. The reordering enables neighboring cells to be stored in contiguous areas of memory as much as possible. The performance of the proposed method is validated by two- and three-dimensional unstructured meshes. According to the memory and spatial distances, the proposed reordering method significantly improves data localities. Consequently, the cache hit rate is increased and the computing efficiency is improved. The proposed reordering method is then applied to large-eddy simulations of flows around an underwater vehicle model with ReL=1.2×106. To fully resolve the near-wall flows, an unstructured mesh consisting of 1.476 billion cells is used, which is partitioned into 12800 subdomains. The computed velocity profiles, pressure and friction coefficients are in good agreement with the experimental measurements. The computational costs are reduced by using the proposed reordering method.

Conformal Marked Bisection for Local Refinement of n-Dimensional Unstructured Simplicial Meshes

We present an n -dimensional marked bisection method for unstructured conformal meshes. We devise the method for local refinement in adaptive n -dimensional applications. To this end, we propose a mesh marking pre-process and three marked bisection stages. The pre-process marks the initial mesh conformingly. Then, in the first n − 1 bisections, the method accumulates in reverse order a list of new vertices. In the second stage, the n -th bisection, the method uses the reversed list to cast the bisected simplices as reflected simplices, a simplex type suitable for newest vertex bisection. In the final stage, beyond the n -th bisection, the method switches to newest vertex bisection. To allow this switch, after the second stage, we check that under uniform bisection the mesh simplices are conformal and reflected. These conditions are sufficient to use newest vertex bisection, a bisection scheme guaranteeing key advantages for local refinement. Finally, the results show that the proposed bisection is well-suited for local refinement of unstructured conformal meshes. • A new multi-stage bisection for n-dimensional unstructured conformal meshes. • Suitable for local refinement. • Leads to conformal and reflected meshes after n uniform refinements. • In the third stage, the method favors conformity, finiteness, stability, and locality.

A coupled level set and volume of fluid method for three dimensional unstructured polyhedral meshes for boiling flows

For the numerical modelling of boiling flows with accurate interface dynamics, a new coupled level set and volume of fluid (CLSVOF) method for three-dimensional unstructured polyhedral meshes has been presented in this paper. An unsplit multidirectional method is used for advecting volume fraction. In this method, the cell vertex velocities interpolated from the cell centres are used to create the flux polyhedron. A total variational diminishing (TVD) scheme is used for the advection of level set function. The level set field is geometrically reinitialized after every time step. The present CLSVOF method is tested against several two as well as three-dimensional advection test cases for both structured and unstructured polyhedral meshes to determine its accuracy and performance. In terms of advection test cases, the suggested method shows good agreement with results of previous studies that used interface reconstruction techniques of higher order. The proposed method is then used to simulate two as well as three-dimensional saturated film boiling over a flat planar surface for both unstructured polyhedral and structured meshes. The obtained results are in accordance with the results available in literature. The present CLSVOF method is also demonstrated for saturated film boiling on a horizontal cylinder in both two and three dimensions. In comparison to the earlier numerical studies, the present results are in good accordance with the available semi-empirical correlations. • A CLSVOF method is developed for boiling flows on 3D unstructured polyhedral meshes. • The proposed boiling flow solver can be used for any complex geometries. • The solver is validated for two-phase flows with and without phase change. • For boiling flows, the present results agree well with semi-empirical correlations.

Comparison of terrain corrections based on the point source and line source DC methods

In the direct current (DC) exploration method, topographic relief distorts the apparent resistivity curve. To eliminate effects of terrain fluctuations, two undulating terrains comprising valleys and ridges were investigated in the present study. An unstructured triangular mesh method in which the wave number k and its coefficient g were obtained using the integral method and the point and line source surveys were conducted using comsol multiphysics. Current sources were evaluated using two-dimensional (2-D) finite element forward modeling, whereas terrain correction was performed using both the comparison and conformal transformation methods. The results reveal comparable theoretical curves for the line and point sources, but quantitative characteristics of the curves differ. The comparison method is suitable for both curves, whereas the conformal transformation method is only applicable to the line source. Even though electric fields associated with the line and point sources differ, the comparison method that is based on the electrical cross-section curve of the line source and the electric profile curve of the point source remains effective.

Test problem of the flow modeling in axial compressor cascades

The flow of gas in the flow path of a gas turbine engine (GTE) is accompanied by a rather complex phenomenon. These are a three-dimensional boundary layer, an incoming vortex, a paired vortex, flow turbulence, aerodynamic wakes behind the trailing edge, separation of the boundary layer from the blade surface, pressure pulsations, uneven and unsteady flow, secondary overflows, changes in the angles of flow exit, etc. Flow R&D of a GTE remains a rather complex process, and requires the use of reliable research methods and techniques. Nowadays, two known methods are used to study a gas flow through the flow path of a GTE ˗ experimental and calculated. Calculated, in turn, can be divided into analytical and numerical. An important stage of the numerical experiment is the solution to test problems for the possibility of setting the parameters of the numerical experiment. In this work, two test tasks were carried out. The object of the research was two compressor cascades, consisting of the identical airfoils series KR-33. The profile chord was 52 mm; the pitch cascade was 52 mm. The difference was in the installation angle of these profiles: variant 1 of the compressor cascade has an installation angle of 63.5º; variant 2 of the compressor cascade has an installation angle of 89.5º. A computational domain was constructed for each compressor cascades of airfoils and consisted of 5 million cells. Air under normal atmospheric conditions was chosen as the working fluid. The flow regime of compressor cascades varied in the range of coefficient λ = 0.26…0.9 and λ = 0.265…0.8, where the coefficient λ is the reduced velocity. The unstructured mesh method with an adaptation for the boundary layer was chosen to construct the computational mesh. Such a combination makes it possible to correctly model the flow in the boundary layer near the walls. The turbulence model SST was taken to close the Navier-Stokes equations. A comparison of the results of numerical and physical experiments for two variants of compressor cascades shows that the flow simulation error is less than 5%. Because of the calculation, the choice of this turbulence model for subsequent studies of the flow in the stages of the compressor, fan, and propfan will be justified.

Fatigue Crack Growth Analysis under Constant Amplitude Loading Using Finite Element Method.

Damage tolerant design relies on accurately predicting the growth rate and path of fatigue cracks under constant and variable amplitude loading. ANSYS Mechanical R19.2 was used to perform a numerical analysis of fatigue crack growth assuming a linear elastic and isotropic material subjected to constant amplitude loading. A novel feature termed Separating Morphing and Adaptive Remeshing Technology (SMART) was used in conjunction with the Unstructured Mesh Method (UMM) to accomplish this goal. For the modified compact tension specimen with a varied pre-crack location, the crack propagation path, stress intensity factors, and fatigue life cycles were predicted for various stress ratio values. The influence of stress ratio on fatigue life cycles and equivalent stress intensity factor was investigated for stress ratios ranging from 0 to 0.8. It was found that fatigue life and von Mises stress distribution are substantially influenced by the stress ratio. The von Mises stress decreased as the stress ratio increased, and the number of fatigue life cycles increased rapidly with the increasing stress ratio. Depending on the pre-crack position, the hole is the primary attraction for the propagation of fatigue cracks, and the crack may either curve its direction and grow towards it, or it might bypass the hole and propagate elsewhere. Experimental and numerical crack growth studies reported in the literature have validated the findings of this simulation in terms of crack propagation paths.

Finite Element Simulation of a Crack Growth in the Presence of a Hole in the Vicinity of the Crack Trajectory.

The aim of this paper was to present a numerical simulation of a crack growth path and associated stress intensity factors (SIFs) for linear elastic material. The influence of the holes’ position and pre-crack locations in the crack growth direction were investigated. For this purpose, ANSYS Mechanical R19.2 was introduced with the use of a new feature known as Separating Morphing and Adaptive Remeshing Technology (SMART) dependent on the Unstructured Mesh Method (UMM), which can reduce the meshing time from up to several days to a few minutes, eliminating long preprocessing sessions. The presence of a hole near a propagating crack causes a deviation in the crack path. If the hole is close enough to the crack path, the crack may stop at the edge of the hole, resulting in crack arrest. The present study was carried out for two geometries, namely a cracked plate with four holes and a plate with a circular hole, and an edge crack with different pre-crack locations. Under linear elastic fracture mechanics (LEFM), the maximum circumferential stress criterion is applied as a direction criterion. Depending on the position of the hole, the results reveal that the crack propagates in the direction of the hole due to the uneven stresses at the crack tip, which are consequences of the hole’s influence. The results of this modeling are validated in terms of crack growth trajectories and SIFs by several crack growth studies reported in the literature that show trustworthy results.

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.

A Compact Subcell WENO Limiting Strategy Using Immediate Neighbors for Runge-Kutta Discontinuous Galerkin Methods for Unstructured Meshes

In this paper, we generalize the compact subcell weighted essentially non oscillatory (CSWENO) limiting strategy for Runge-Kutta discontinuous Galerkin method developed recently in [1] for structured meshes to unstructured triangular meshes. The main idea of the limiting strategy is to divide the immediate neighbors of a given cell as subcells into the required stencil and to use a WENO reconstruction for limiting. This strategy can be applied for any type of WENO reconstruction. We have used the WENO reconstruction proposed in [2] and provided accuracy tests and results for two-dimensional Burgers’ equation and two dimensional Euler equations to illustrate the performance of this limiting strategy.

Third order asynchronous time integration for gas dynamics

A third order Asynchronous Runge Kutta method is introduced. The method can handle strong shock waves using independent local time stepping at the cell level. This method is then coupled with a novel third order limiting strategy based on an artificial viscosity-like sensor. The limiter is then used in the framework of the multi-slope MUSCL method for unstructured meshes. This integration method can also advantageously be coupled with Asynchronous Adaptive Mesh Refinement to treat compressible, reacting, multi-component flow problems. The accuracy and acceleration properties of the method are shown on a wide range of numerical tests.

Mesh-free radial-basis function generated finite differences and its application in full-waveform inversion

As the key point of full-waveform inversion (FWI), numerical solution of wave equation is required to simulate the forward propagated and adjoint wavefield. When traditional regular grids are used for forward modelling, scattering artifacts may occur due to the stepped approximation of layer interfaces and rugged topography. Unstructured mesh or irregular grids method can achieve certain geometric flexibility, however, its algorithm is quite complex. Mesh-free FWI can effectively reduce the scattered artifacts under regular grids and avoid the extra computation in the process of irregular grids generation. For the implementation of mesh-free FWI method, an algorithm with fast generation of node distributions is used to discretize the velocity model, radial-basis function generated finite difference is used to realise seismic wave propagation numerical simulation, and Limited-memory BFGS (L-BFGS) algorithm is used for iteration. The mesh-free FWI method we proposed achieves flexibility of simulation region and abundant wavefield information. It reduces the storage required for FWI and illustrates the applicability of high-precision reconstruction of underground velocity in the case of rugged topography, which can provide more accurate velocity information for oil and gas exploration under complex geological conditions.

Adaptive deformation of 3D unstructured meshes with curved body fitted boundaries with application to unsteady compressible flows

We present an adaptive moving mesh method for unstructured meshes which is a three-dimensional extension of the previous works of Ceniceros et al. [10], Tang et al. [40] and Chen et al. [11]. The iterative solution of a variable diffusion Laplacian model on the reference domain is used to adapt the mesh to moving sharp solution fronts while imposing slip conditions for the displacements on curved boundary surfaces. To this aim, we present an approach to project the nodes on a given curved geometry, as well as an a-posteriori limiter for the nodal displacements developed to guarantee the validity of the adapted mesh also over non-convex curved boundaries with singularities.We validate the method on analytical test cases, and we show its application to two and three-dimensional unsteady compressible flows by coupling it to a second order conservative Arbitrary Lagrangian-Eulerian flow solver.

A Near-Shore Linear Wave Model with the Mixed Finite Volume and Finite Difference Unstructured Mesh Method

The near-shore and estuary environment is characterized by complex natural processes. A prominent feature is the wind-generated waves, which transfer energy and lead to various phenomena not observed where the hydrodynamics is dictated only by currents. Over the past several decades, numerical models have been developed to predict the wave and current state and their interactions. Most models, however, have relied on the two-model approach in which the wave model is developed independently of the current model and the two are coupled together through a separate steering module. In this study, a new wave model is developed and embedded in an existing two-dimensional (2D) depth-integrated current model, SRH-2D. The work leads to a new wave–current model based on the one-model approach. The physical processes of the new wave model are based on the latest third-generation formulation in which the spectral wave action balance equation is solved so that the spectrum shape is not pre-imposed and the non-linear effects are not parameterized. New contributions of the present study lie primarily in the numerical method adopted, which include: (a) a new operator-splitting method that allows an implicit solution of the wave action equation in the geographical space; (b) mixed finite volume and finite difference method; (c) unstructured polygonal mesh in the geographical space; and (d) a single mesh for both the wave and current models that paves the way for the use of the one-model approach. An advantage of the present model is that the propagation of waves from deep water to shallow water in near-shore and the interaction between waves and river inflows may be carried out seamlessly. Tedious interpolations and the so-called multi-model steering operation adopted by many existing models are avoided. As a result, the underlying interpolation errors and information loss due to matching between two meshes are avoided, leading to an increased computational efficiency and accuracy. The new wave model is developed and verified using a number of cases. The verified near-shore wave processes include wave shoaling, refraction, wave breaking and diffraction. The predicted model results compare well with the analytical solution or measured data for all cases.

Acceleration of NOISEtte Code for Scale-Resolving Supercomputer Simulations of Turbulent Flows

The present work is devoted to accelerating the NOISEtte code and lowering its memory consumption. This code for scale-resolving supercomputer simulations of compressible turbulent flows is based on higher-accuracy methods for unstructured mixed-element meshes and hierarchical MPI $$+$$ OpenMP parallelization for cluster systems with manycore processors. We demonstrate modifications of the underlying numerical method and its parallel implementation, which consist, in particular, in using a simplified approximation method for viscous fluxes and mixed floating-point precision. The modified version has been tested on several representative cases. The performance measurements and validation results are presented.

A scalable framework for the partitioned solution of fluid–structure interaction problems

In this work, we present a scalable and efficient parallel solver for the partitioned solution of fluid–structure interaction problems through multi-code coupling. Two instances of an in-house parallel software, TermoFluids, are used to solve the fluid and the structural sub-problems, coupled together on the interface via the preCICE coupling library. For fluid flow, the Arbitrary Lagrangian–Eulerian form of the Navier–Stokes equations is solved on an unstructured conforming grid using a second-order finite-volume discretization. A parallel dynamic mesh method for unstructured meshes is used to track the moving boundary. For the structural problem, the nonlinear elastodynamics equations are solved on an unstructured grid using a second-order finite-volume method. A semi-implicit FSI coupling method is used which segregates the fluid pressure term and couples it strongly to the structure, while the remaining fluid terms and the geometrical nonlinearities are only loosely coupled. A robust and advanced multi-vector quasi-Newton method is used for the coupling iterations between the solvers. Both the fluid and the structural solver use distributed-memory parallelism. The intra-solver communication required for data update in the solution process is carried out using non-blocking point-to-point communicators. The inter-code communication is fully parallel and point-to-point, avoiding any central communication unit. Inside each single-physics solver, the load is balanced by dividing the computational domain into fairly equal blocks for each process. Additionally, a load balancing model is used at the inter-code level to minimize the overall idle time of the processes. Two practical test cases in the context of hemodynamics are studied, demonstrating the accuracy and computational efficiency of the coupled solver. Strong scalability test results show a parallel efficiency of 83% on 10,080 CPU cores.

An unstructured mesh method for numerical simulation of violent sloshing flows

An unstructured mesh Reynolds-averaged Navier-Stokes (RANS) solver has been developed for numerical simulation of violent sloshing flows inside a tank with complicated inner structures. The numerical solver employs the unstructured multi-dimensional tangent hyperbolic interface capturing method (UMTHINC) for free-surface capturing combined with various turbulence models. The sloshing motion is numerically modeled using the body-force method which introduces a source term into the momentum equation corresponding to the tank motion profile. Numerical simulations of the tank sloshing problems are performed for different test cases with various oscillation frequencies. The performance of the interface capturing method has been discussed and the effect of turbulence model choice on loading predictions is highlighted by studying several RANS models and analyzing its effect on fluid motion and impact pressure. Numerical simulations of the sloshing inside the tank with a vertical baffle has also been conducted and a discussion is provided on different numerical treatment of the baffle.

Application of R2S unstructured tetrahedral mesh method to radioactive concrete structure dismantling using AETIUS/FISPACT codes

Application of R2S unstructured tetrahedral mesh method to radioactive concrete structure dismantling using AETIUS/FISPACT codes

Development and testing of an unstructured mesh method for whole plasma gyrokinetic simulations in realistic tokamak geometry

In this work, we have formulated and implemented a mixed unstructured mesh-based finite element–Fourier decomposition scheme for gyrokinetic simulations in realistic tokamak geometry. An efficient particle positioning (particle-triangle mapping) scheme for the charge deposition and field scattering using an intermediate grid as the search index for triangles has been implemented, and a significant speed-up by a factor of ∼30 is observed as compared with the brute force scheme for a medium-size simulation. The TRIMEG (TRIangular MEsh based Gyrokinetic) code has been developed. As an application, the ion temperature gradient (ITG) mode is simulated using the simplified gyrokinetic Vlasov-Poisson model. Our simulation and that using the ORB5 code for the DIII-D Cyclone case show reasonable agreement. As an additional application, ITG simulations using an ASDEX Upgrade equilibrium have been performed with density and temperature gradient profiles similar to the Cyclone case. Capabilities of the TRIMEG code for simulations with realistic experimental equilibria in the plasma core and in the whole plasma volume with open field lines are demonstrated.

Finite element reverse time migration imaging in tunnels using an unstructured mesh

Wave field extrapolation is critical in reverse time migration (RTM). At present, wavefield extrapolation in RTM imaging for tunnels is mostly carried out via the finite difference method. However, complex tunnel models, such as those for karst and fault fracture zones, are constructed using regular grids with straight curves which can easily cause numerical dispersion and reduce imaging accuracy. In this study, the wavefield extrapolation for tunnel RTM was conducted using the finite element method, where an unstructured mesh is employed as the body-fitted partition in a complex model. The Poynting vector calculation equation suitable for the unstructured mesh finite element method was established to suppress low-frequency noise interference. The tunnel space was considered during the wavefield extrapolation to suppress mirror artefacts by using the flexibility of mesh generation. Finally, the influence of the survey layouts (one-sidewall and two-sidewall) on the tunnel imaging results was explored. The RTM results for a simple tunnel model with an inclined interface show that the method based on unstructured meshes can effectively suppress low-frequency noise and mirror artefacts, thus obtaining clearer imaging results. Also, the two-sidewall tunnel survey layout more accurately obtains the real position of the inclined interface ahead of the tunnel face. Complex tunnel numerical modelling and actual data migration results further illustrate the effectiveness of the finite element unstructured mesh method.