Three-dimensional Unstructured Grid Research Articles

A high-performance ray tracing particle tracking model for the simulation of microplastics in inland and coastal aquatic environments

In this study, we present a high-performance Particle Tracking Model (PTM) designed for simulating any type of particles, with a focus on microplastics. The PTM is efficient compared to existing models, parallelized, and utilizes a ray tracing algorithm incorporating both ray reflection and ray refraction in order to traverse particles as well as find the location of each particle over three-dimensional unstructured grids. Various numerical corrections are implemented in the model to address computational round-off errors and discontinuities in the water surface level of the input hydrodynamic models. To increase the accuracy of the model, partially reflective boundary conditions are imposed as well as the capability to simulate microplastics beaching and washout in very shallow areas or dry computational cells. Several tests are conducted to study the performance, scalability, and accuracy of the model. The proposed model is tested with over 3.88 billion double-precision particles on three-dimensional computational grids with up to approximately one million cells. The tests show that the ray tracing approach is efficient, achieves over 17× faster runtime, and offers greater accuracy compared to using an auxiliary grid for particle location finding. For larger timesteps, the ray tracing PTM with refraction shows improved accuracy compared to the ray tracing PTM without refraction. The model's capabilities are tested in a real-world case study over the Saguenay Fjord, Quebec, Canada. The model is utilized to reproduce the paths of five surface drifters. A second numerical test is conducted in the Fjord and high particle concentration areas are identified.

Influence of freshwater on the vertical structure of tidal currents: A case study of the Pearl River Estuary

Field observations in the Pearl River Estuary (PRE) indicate that vertical structures of tidal currents vary in different regions, which is associated with freshwater-induced stratification. A three-dimensional unstructured grid model (PRE-model) based on FVCOM is developed to study the mechanism of vertical structural changes in tidal currents. With the effect of freshwater, the amplitude of tidal currents increases in the upper layers and decreases in the bottom layers, and in regions with geometrical complexity, it is maximum in the middle depths. Momentum analysis indicates that vertical friction (VF), pressure gradient forces (PGF), and momentum advection (ADV) are the main factors leading to changes in tidal vertical structures. Variations of VF induced by stratification lead to an increase of tidal currents amplitude in the upper layers while a decrease in the bottom layers. Changes in PGF and ADV can also have significant impacts on tidal currents. Tidal frequency variations of density gradients result in pronounced tidal frequency baroclinic PGF in the bottom depths and enlarge total PGF. The amplitude of tidal currents increases at corresponding depths, which leads to subsurface maxima of tidal currents. ADV is special as its phase is variable relative to tidal currents, which can enhance or weaken tidal currents in different regions. The generation of tidal frequency baroclinic PGF is highly correlated with nonlinear processes, and the horizontal advection is considered the primary source of baroclinic PGF. The similar sources of ADV and baroclinic PGF also make them dominant in regions with geometrical complexity or large river plumes.

A novel approach to the characteristic splitting scheme for mildly compressible flows based on the weighted averaged flux method

In the present work we improve the characteristic splitting approach for computing mildly compressible flows. This splitting approach is consisted of two separate steps namely an advective step and a purely hyperbolic, acoustic step. Typically, a pressure correction method is used for solving the acoustic step which may lead to overly dispersive, incorrect results. As a remedy to this issue, a novel solution approach on the basis of the weighted averaged flux method (WAF) is proposed, which solves the non-conservative, hyperbolic equations of the acoustic step directly. The stability and accuracy of this novel WAF method is demonstrated and an implicit, monotone formulation for three-dimensional unstructured grids is given. The simulation of the non-reacting flow in a swirl burner proves the applicability of the method.

A Unified Grid Approach Using Hamiltonian Paths for Computing Aerodynamic Flows

A solution algorithm using Hamiltonian paths is presented as a unified grid approach for rotorcraft applications. Hidden line structures are robustly identified on general two- and three-dimensional unstructured grids with mixed elements, providing a framework for line-based solvers. A pure quadrilateral/hexahedral mesh is a prerequisite for line identification and enables approximate factorisation along the lines. The numerical efficiency obtained using the line-implicit method on various unstructured grids is better than that of the point-implicit method. Both finite-difference and gradient reconstructions are possible regardless of grid type. A combined reconstruction method is applied, which uses different reconstructions simultaneously but for different grid directions. Finally, the solution convergence rate is further improved using a preconditioned generalized minimal residual method (GMRES), where the preconditioning step is performed using the efficient line-implicit method.

Leading-Edge separation behaviors in SA RANS and SA-based DDES: Simple modifications for improved prediction

In this study, delayed detached-eddy simulations (DDESs) based on the Spalart–Allmaras turbulence model are investigated for separation flows. Three simple modifications are considered: the Reynolds-averaged Navier–Stokes (RANS) turbulence model coefficient, Crot, is calibrated to achieve a better leading-edge separation prediction in DDES; the large-eddy simulation (LES) coefficient, CDES, is assessed to obtain better dissipation control in DDES; and dirty-cell treatments in three-dimensional unstructured grids are conducted for a smooth LES/RANS transition. Numerical results confirm the effects of the three aforementioned steps, such as the reproducibility of the measured pressure distribution over the main wing in unsteady turbulence simulations of low-speed buffet around the NASA Common Research Model. Thus, these modifications will potentially serve as good alternatives, without major programming efforts, to the conventional approaches for practitioners.

Research on Internal Structure and Mechanism of Landslide Based on Hydrogeophysical Investigation (Quan’an Landslide, Southwest China)

The survey area is located in the planning area of Longquan national urban park, with frequent human activities, numerous water conservancy, transportation projects, and frequent geological disasters such as landslides. The Red Mudstone has low strength and easy to soften in the case of water, and it is very prone to landslide in rainy season. At present, there are many studies on Red Mudstone Landslides, but most of them are analyzed by geological means, and the monitoring process is also dominated by surface deformation and settlement; there is less analysis with hydrogeological that is caused by rainfall and human activities. For Red Mudstone Landslides, to effectively reveal and analyze the process of the Slip Mechanism, we need to carry out the characteristics of hydrogeological structure and underground physical structure, and compare with surface monitoring and point geological structure. In this study, a one-year field survey and hydrogeophysical survey were carried out. Combined with the characteristics of environmental geology, the geophysical forward modeling problem based on finite element method was used to verify the influence of rainfall on the electrical characteristics of underground media. The smoothness constrained least square method and three-dimensional unstructured grid method are used to interpret the ERT data, analyze the abnormal patterns of electrical structure of landslide in different seasons, and correspond well with the GPR data. According to the characteristics of surface vegetation and weathering, as well as the displacement and settlement monitoring after landslide, the spatial characteristics of red bed landslide are revealed, and the relationship between landslide, rainfall, and human activities is clarified.

PorousMultiphaseFoam v2107: An open-source tool for modeling saturated/unsaturated water flows and solute transfers at watershed scale

The first releases of porousMultiphaseFoam proposed an open-source software suite to solve the equations for multiphase flow (generalized Darcy’s law) in porous media or groundwater flows (Richards' equation) by taking advantage of OpenFOAM, a finite volume platform with automatic discretization on three-dimensional unstructured grids and good parallel efficiency. Recently, the porousMultiphaseFoam toolbox has been confronted with complex cases of fast water flows and solute transfers in realistic hydrological configurations with variable forcing conditions (heterogeneous infiltration and local tracer injection). Several developments have been carried out to make it possible to simulate those cases, which extend the toolbox with: (i) a set of solvers dedicated to groundwater flows, including coupled water flow and solute transport and simplified 2D approaches, (ii) improved numerical techniques for problems with strong non-linearities, (iii) libraries/executables for pre-processing of input data (geographical information and time-variable forcing terms) and (iv) passive or coupled scalar transport (tracer) with groundwater solvers that support any number of species. New solvers are validated on several (un-)saturated configurations by a direct comparison with a well validated finite element code. Program summaryProgram title: porousMultiphaseFoam v2107CPC Library link to program files:https://doi.org/10.17632/hphn58ksfy.1Developer's repository link:https://github.com/phorgue/porousMultiphaseFoam.gitLicensing provisions: GNU GPLv3Programming language: C++ / OpenFOAMJournal reference of previous version: Computer Physics Communications 187 (2015) 217-226Does the new version supersede the previous version?: YesReasons for the new version: Multiple new features of the toolbox dedicated to groundwater flows (with pre-processing tools)Summary of revisions:–Solvers:–groundwaterFoam/stationaryGroundwaterFoam: new unsaturated flow (transient/stationary) solvers in porous media (Richards' equation) using Picard or Newton's method for linearization.–groundwater2DFoam/stationaryGroundwater2DFoam: new 2D (transient/stationary) solver for saturated flow in porous media.–porousScalarTransportFoam/porousScalarTransport2DFoam: new passive multi-scalar transport solvers on pre-computed flow fields (3D unsaturated or 2D saturated fields).–groundwaterTransportFoam/groundwaterTransport2DFoam: new solvers coupling flow modeling (2D saturated or 3D unsaturated) with multi-scalar tracers transports.–Improved numerical techniques–Timestep management: time-stepping is now based on the temporal truncation of the time scheme used (backward Euler 1st and 2nd order, Crank-Nicolson).–Linearization techniques: problems of unsaturated flow with strong non-linearities can now be solved using an algorithm based on Newton's method.–Libraries:–numericalMethods: the EulerD3dt3Scheme class allows computation of the 3rd-order time derivative to estimate the truncation error and the JacobianMatrix class computes the Jacobian using finite differencing (expensive method used only for debugging).–toolsGIS: new dynamic library for managing GIS (Geographical Information System) files and event files. Events are variable and localized source terms for fluid or scalar transport.–Ippisch: an improved two-phase model for relative permeability and capillary pressure.–porousBoundaryConditions: several new boundary conditions have been added to handle heterogeneous pressure head boundary conditions and variable fluid or tracer injections (using event files).–Utilities:–setBoundaryHeadPressure: pressure head initializer for boundary conditions using uniform value of GIS files.–setFieldsFromDEM/setFieldsFromXY: heterogeneous initializer for internal fields, similar to the classical OpenFOAM setFields, but using ordered (DEM) or unordered (XY) grid files.–darcyFoam: simple utility to calculate a single-phase flow in porous media.Nature of problem: The porousMultiphaseFoam toolbox was initially released with generic two-phase solvers for flow in porous media. Developments were carried out to model more specifically hydrogeological flows by including a groundwaterFoam solver for Richards' equation. However, many features required to simulate realistic configurations, such as event management for variable and heterogeneous forcing terms (infiltration / scalar source term) or suitable numerical techniques for complex configurations (high rate injection for unsaturated flow for example), were still missing. Moreover, the 2D approach with integration of vertical properties (for flow and tracer) was not present even though this is an indispensable tool for groundwater flow modeling due to its ease of implementation and its low computation cost.Solution method: Improved numerical techniques have been developed to solve realistic flows by handling strong non-linearities with Newton's method, and a wide range of time scales with time-stepping based on time truncation errors. Various solvers for groundwater flows have been developed to handle cases under different assumptions, including the aforementioned 2D approaches. Variants of these solvers were also developed to simultaneously solve the passive transport of any number of scalars (tracers) by the flow. A dynamic library has been developed to pre-process input data: event information for variable conditions, GIS file for spatial information.Additional comments including restrictions and unusual features: porousMultiphaseFoam v2107 requires an installation of OpenFOAM-v9. Dedicated branches are available on the developer's repository for compatibility with other versions of OpenFOAM. The following versions are compatible with the current version of porousMultiphaseFoam: v7, v8, v1906, v2006 and v2106. Older branches may be found in the repository link but do not contain all features.

An explicit iterative scheme for 3D multicomponent heat conducting flow simulation

This paper presents the development and testing of time integration scheme for the system of hydrodynamic equations of gas mixture. These equations take into account the phenomena of multicomponent diffusion and heat transfer. The governing equation system is discretized by the finite volume approach on three-dimensional unstructured grids. According to the algorithm, computation of any single time step is split into the sequence of hyperbolic and parabolic stages. The hyperbolic subtask is solved using the Godunov-type scheme. The parabolic subtask is solved by the explicit iterative Chebyshev scheme, which is algorithmically simple and does not involve tuning parameters. This stage addresses dissipative fluxes (viscosity, multicomponent diffusion and thermal conductivity). The number of the explicit iterations is determined by the convective time step and by the upper bound for the discrete diffusion operator. The resulting scheme ensures the fulfillment of the conservation laws at the discrete level. The computer code can be used in highly parallel computing for large-scale simulation. The proposed approach is recommended for applied problems in which convective and dissipative processes are in close interaction, particularly for problems of plasma physics and astrophysics.

Numerical simulation of boiling on unstructured grids

A numerical method for the simulation of multiphase flows with phase change on unstructured grids is presented. Based on the work of Tanguy et al. [31] using a Level Set/Ghost Fluid Method coupling for two-dimensional axisymmetric cartesian grids, we extend the method to two- and three-dimensional unstructured grids with the aim of taking a step towards realistic boiling simulations in industrial context. The mass transfer rate at the interface accounting for phase change is computed as a function of the liquid and vapor heat fluxes at the interface and of the latent heat of the fluid by means of a new framework improving the accuracy of differential operators. The mass transfer rate is then used in the projection method to solve Navier-Stokes equations and in the advection equation of the Level Set function to account for the interface movement due to phase change. An immersed Dirichlet boundary condition is imposed at the interface to ensure that boiling always occurs at saturation temperature. We demonstrate the accuracy of our method first in the case of a static growing bubble with a fixed constant mass transfer rate, and second with a mass transfer rate computed from the thermal fluxes at the interface. In both cases, the bubble radius at final time converges with grid refinement towards the theoretical value.

Three-dimensional unstructured gridding for complex wells and geological features in subsurface reservoirs, with CVD-MPFA discretization performance

Grid generation for reservoir simulation, must honour classical key geological features and multilateral wells. The features to be honoured are classified into two groups; (1) involving layers, faults, pinchouts and fractures, and (2) involving well distributions. In the former, control-volume boundary aligned grids (BAGs) are required, while in the latter, control-point (defined as the centroid of the control-volume) well aligned grids (WAGs) are required. Depending on discretization method type and formulation, a choice of control-point and control-volume type is made, i.e. for a cell-centered method the primal grid cells act as control-volumes, otherwise for a vertex-centered method the dual-grid cells act as control-volumes. Novel three-dimensional unstructured grid generation methods are proposed that automate control-volume boundary alignment to geological features and control point alignment to complex wells, yielding essentially perpendicular bisector (PEBI) meshes either with respect to primal or dual-cells depending on grid type. Both grid types use tetrahedra, pyramids, prisms and hexahedra as grid elements. Primal-cell feature aligned grids are generated using special boundary surface protection techniques together with constrained cell-centered well trajectory alignment. Dual-cell feature aligned grids are generated from underlying primal-meshes, whereby features are protected such that dual-cell control-volume faces are aligned with interior feature boundaries, together with protected vertex-centered (control point) well trajectory alignment. The novel methods of grid generation presented enable practical application of both method types in 3-D for the first time. The primal and dual grids generated here demonstrate the gridding methods, and enable the first comparative performance study of cell-vertex versus cell-centered control-volume distributed multi-point flux approximation (CVD-MPFA) finite-volume formulations using equivalent mesh resolution on challenging problems in 3-D. Pressure fields computed by the cell-centered and vertex-centered CVD-MPFA schemes are compared and contrasted relative to the respective degrees of freedom employed, and demonstrate the relative benefits of each approximation type. Stability limits of the methods are also explored. For a given mesh the cell-vertex method uses approximately a fifth of the unknowns used by a cell-centered method and proves to be the most beneficial with respect to accuracy and efficiency. Numerical results show that vertex-centered CVD-MPFA methods outperform cell-centered CVD-MPFA method.

Three-Dimensional Unstructured Grid Finite-Volume Model for Coastal and Estuarine Circulation and Its Application

We developed a three-dimensional unstructured grid coastal and estuarine circulation model, named the General Ocean Model (GOM). Combining the finite volume and finite difference methods, GOM achieved both the exact conservation and computational efficiency. The propagation term was implemented by a semi-implicit numerical scheme, the so-called θ scheme, and the time-explicit Eulerian–Lagrangian method was used to discretize the nonlinear advection term to remove the major limitation of the time step, which appears when solving shallow water equations, by the Courant–Friedrichs–Lewy stability condition. Because the GOM uses orthogonal unstructured computational grids, allowing both triangular and quadrilateral grids, considerable flexibility to resolve complex coastal boundaries is allowed without any transformation of governing equations. The GOM was successfully verified with five analytical solutions, and it was also validated when applied to the Texas coast, showing an overall skill value of 0.951. The verification results showed that the algorithm used in GOM was correctly coded, and it is efficient and robust.

Research on remote control algorithm for parallel implicit domain robot patrol inspection on 3D unstructured grid

Aiming at the disadvantages of structural meshes that are difficult to deal with complex shapes and unstructured meshes, it is impossible to calculate the viscous flow with boundary layers. A parallel implicit algorithm based on three-dimensional unstructured meshes is developed. The turbulence model adopts the k − π turbulence model. Due to the difficulty of the LU-SGS parallel equivalent model in time advancement, a three-dimensional unstructured grid DSMC parallel algorithm is proposed. Under the unstructured grid dynamic partitioning strategy, each sub-area is guaranteed. The number of molecules is roughly equal. Based on the implicit algorithm of DP-LUR (data-parallel lower–upper relaxation) format, the remote control combination model of robot inspection is calculated, and the mutual interference flow problem during the inspection process is accurately simulated. The operator realizes the remote control of the inspection robot through the live image transmitted by the network. The actual operation shows that the system can remotely access the service system and message transmission of the inspection robot in the state of the sub-structure grid, and successfully solve the robot tour. Check the complex shape viscous flow field calculation and efficiency problems that are difficult to handle in remote control systems.

Application of discontinuous Galerkin method in supersonic and hypersonic gas flows

Most high-order methods often suffer from two- and three-dimensional unstructured grids, particularly, for supersonic and hypersonic gas flows. We applied a high-order mixed-modal discontinuous Galerkin method with a coupled slope limiter to investigate multidimensional cases of supersonic and hypersonic gas flows. Furthermore, we provide detailed implementations and validations of two- and three-dimensional problems. Examples include double Mach reflection problems and supersonic and hypersonic gas flows around a cylinder. In addition, we provide case studies of a 3D hypersonic vehicle to evaluate its computational performance on complex hypersonic gas flows. This study can be regarded as an attempt to apply the discontinuous Galerkin method to engineering problems.

Postlimiters and Simple Dirty-Cell Detection for Three-Dimensional Unstructured (Unlimited) Aerodynamic Simulations

The postlimiter (simple a posteriori slope limiter) is an anti-slope-limiting mechanism to preserve nominal second order in space as much as possible. This technique has been demonstrated to increase resolutions of two-dimensional simulations up to four times in each dimension [Kitamura, K., and Hashimoto, A., “Simple a posteriori Slope Limiter (Post Limiter) for High Resolution and Efficient Flow Computations,” Journal of Computational Physics, Vol. 341, July 2017, pp. 313–340]. This paper extends the postlimiter to three dimensions with an emphasis on ”dirty” (meaning ill-shaped) cells, which arise in practical three-dimensional (3-D) unstructured grids over complex geometries. Gradient accuracy is known to significantly deteriorate on dirty cells, and a slope limiter needs to be applied. However, the original postlimiter does not recognize dirty cells and deactivates a slope limiter. To address this issue, a simple dirty-cell detection method is proposed and incorporated into the postlimiter. The 3-D version of postlimiter (referred to as “postlimiter 3”) is successfully incorporated into fast aerodynamic routine (FaSTAR), a 3-D unstructured grid flow solver is developed at the Japan Aerospace Exploration Agency. Postlimiter 3 can handle general 3-D unstructured grids. Numerical examples support its efficiency, accuracy, robustness, and applicability to a wide spectrum of aerodynamic problems of high engineering importance.

Development and convergence analysis of an effective and robust implicit Euler solver for 3D unstructured grids

This paper reports the development and convergence analysis in steady-state of an effective and robust implicit finite-volume solver for compressible Euler equations on three-dimensional unstructured grids. A second-order upwind scheme (MUSCL) was employed based on Roe's approximate Flux-Difference Scheme (FDS) by using Venkatrakishnan flux limiters. The construction of the linear system for the implicit scheme was performed by applying the backward Euler on the left-hand side of the conservation equation and Newton-type linearization on the right-hand side. The Jacobian matrix that resulted from the linearization process was computed analytically using Roe flux terms. In this phase, the defect-correction technique was employed allowing effective time-dependent computations by an implicit time-integration scheme. In this approach, the flux integral on the right-hand side is computed based on a high-order of accuracy whilst the left-hand side the Jacobian is performed based on the low-order. The resulting sparse and large system of linear equations is solved by a sequential Gauss–Seidel iterative method. Simulations were performed and the developed implicit defect-correction solver was validated and verified. In addition, convergence analysis comparing the implicit solver and the explicit Runge–Kutta of 5-steps using Implicit Residual Smoothing (IRS) were performed showing the significant speed-up of the implicit solver over the explicit one. Simulations were performed for case studies to demonstrate the robustness of the developed implicit defect-correction solver in solving typical problems of aerodynamic involving transonic condition and shock wave captures for internal and external flows. Finally, the main particularities of the implicit scheme were investigated and discussed considering the simulation results, showing also its capacity to serve as an effective preconditioner (start-up method) to other implicit techniques.

An Automatic Wall Treatment for Spalart–Allmaras Turbulence Model

The Spalart–Allmaras (SA) is one of the most popular turbulence models in the aerospace computational fluid dynamics (CFD) community. In its original (low-Reynolds number) formulation, it requires a very tight grid spacing near the wall to resolve the high flow gradients. However, the use of wall functions with an automatic feature of switching from the wall function to the low-Reynolds number approach is an effective solution to this problem. In this work, we extend Menter's automatic wall treatment (AWT), devised for the k–ω-shear stress transport (SST), to the SA model in our in-house developed three-dimensional unstructured grid density-based CFD solver. It is shown, for both momentum and energy equations, that the formulation gives excellent predictions with low sensitivity to the grid spacing near the wall and allows the first grid point to be placed at y+ as high as 150 without loss of accuracy, even for the curved walls. In practical terms, this means a near-wall grid 10–30 times as coarse as that required in the original model would be sufficient for the computations.

A TVD scheme for 3d unstructured grids applied to compositional reservoir simulation

Abstract In reducing the grid orientation effect for the numerical solution of partial differential equations, interpolation functions play an important role when the advective transport of the governing equations is considered. This is due to the fact that, in general, the unknowns are evaluated in the vertices of the elements and such properties must be extrapolated to inner parts of the elements. First-order schemes, such as upwind, are the easiest methods to use for performing the extrapolation of the properties. However, such methods introduce a large amount of numerical diffusion in the solution. A few higher-order interpolation schemes, on the other hand, are capable of providing solutions free of numerical diffusion, increasing the accuracy of the method and reducing the computational efforts required. In this work, we investigate the TVD interpolation scheme for three-dimensional unstructured grids in conjunction with Element-based Finite Volume Method (EbFVM) using four types of elements: hexahedron, tetrahedron, prism and pyramid.

Numerical study of flow in the stage of an axial compressor with different topology of computational grid

We conducted a series of calculations with the models of turbulent viscosity k–e, SST and three variants of three-dimensional unstructured computational grids. For each variant of the computational grid we calculated each of the two models of turbulent viscosity at axial velocity at input from 110 to 150 m/s. Comparison of results of numerical experiments with data of the physical experimental studies revealed that an error of the computational research is 0.3...8.6 %. Results of the study showed that at the first phase of calculation of the stage of an axial compressor one can recommend using the model of turbulent viscosity k–e and the coarse computational grid. To solve the problems on internal aerodynamics of compressors taking into account the flow in the near-border layer and aerodynamic trail, it is expedient to employ the model of turbulent viscosity SST and the fine adaptive grid.

An interpolation-free ALE scheme for unsteady inviscid flows computations with large boundary displacements over three-dimensional adaptive grids

A novel strategy to solve the finite volume discretization of the unsteady Euler equations within the Arbitrary Lagrangian–Eulerian framework over tetrahedral adaptive grids is proposed. The volume changes due to local mesh adaptation are treated as continuous deformations of the finite volumes and they are taken into account by adding fictitious numerical fluxes to the governing equation. This peculiar interpretation enables to avoid any explicit interpolation of the solution between different grids and to compute grid velocities so that the Geometric Conservation Law is automatically fulfilled also for connectivity changes. The solution on the new grid is obtained through standard ALE techniques, thus preserving the underlying scheme properties, such as conservativeness, stability and monotonicity. The adaptation procedure includes node insertion, node deletion, edge swapping and points relocation and it is exploited both to enhance grid quality after the boundary movement and to modify the grid spacing to increase solution accuracy. The presented approach is assessed by three-dimensional simulations of steady and unsteady flow fields. The capability of dealing with large boundary displacements is demonstrated by computing the flow around the translating infinite- and finite-span NACA 0012 wing moving through the domain at the flight speed. The proposed adaptive scheme is applied also to the simulation of a pitching infinite-span wing, where the bi-dimensional character of the flow is well reproduced despite the three-dimensional unstructured grid. Finally, the scheme is exploited in a piston-induced shock-tube problem to take into account simultaneously the large deformation of the domain and the shock wave. In all tests, mesh adaptation plays a crucial role.

3D Voronoi grid dedicated software for modeling gas migration in deep layered sedimentary formations with TOUGH2-TMGAS

As is known, a full three-dimensional (3D) unstructured grid permits a great degree of flexibility when performing accurate numerical reservoir simulations. However, when the Integral Finite Difference Method (IFDM) is used for spatial discretization, constraints (arising from the required orthogonality between the segment connecting the blocks nodes and the interface area between blocks) pose difficulties in the creation of grids with irregular shaped blocks. The full 3D Voronoi approach guarantees the respect of IFDM constraints and allows generation of grids conforming to geological formations and structural objects and at the same time higher grid resolution in volumes of interest. In this work, we present dedicated pre- and post-processing gridding software tools for the TOUGH family of numerical reservoir simulators, developed by the Geothermal Research Group of the DICAM Department, University of Bologna. VORO2MESH is a new software coded in C++, based on the voro++ library, allowing computation of the 3D Voronoi tessellation for a given domain and the creation of a ready to use TOUGH2 MESH file. If a set of geological surfaces is available, the software can directly generate the set of Voronoi seed points used for tessellation. In order to reduce the number of connections and so to decrease computation time, VORO2MESH can produce a mixed grid with regular blocks (orthogonal prisms) and irregular blocks (polyhedron Voronoi blocks) at the point of contact between different geological formations. In order to visualize 3D Voronoi grids together with the results of numerical simulations, the functionality of the TOUGH2Viewer post-processor has been extended. We describe an application of VORO2MESH and TOUGH2Viewer to validate the two tools. The case study deals with the simulation of the migration of gases in deep layered sedimentary formations at basin scale using TOUGH2-TMGAS. A comparison between the simulation performances of unstructured and structured grids is presented.