Nonlinear Finite Volume Method for 3D Discrete Fracture-Matrix Simulations

SPE Journal ◽  
2020 ◽  
Vol 25 (04) ◽  
pp. 2079-2097 ◽  
Author(s):  
Wenjuan Zhang ◽  
Mohammed Al Kobaisi
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Computational Domain ◽  
Matrix Domain ◽  
Fracture Planes ◽  
Flux Approximation ◽  
Discrete Fracture ◽  
The Matrix ◽  
Permeability Anisotropy ◽  
Volume Method

Summary We present a lower dimensional discrete fracture-matrix (DFM) model for general nonorthogonal meshes populated by anisotropic permeability tensors in 3D spatial dimension. The discrete fractures are represented as 2D planes embedded in a 3D matrix domain and serve as internal boundaries for conforming meshing of the entire computational domain. The nonlinear finite volume method (FVM) is used to derive flux for both matrix-matrix connections and fracture-fracture connections to account for permeability anisotropy in the matrix and inside the fracture planes, whereas the linear two-point flux approximation (TPFA) is used to couple the matrix and fracture together. The nonlinear method proceeds by first constructing two one-sided fluxes for a connection, and then a unique flux is obtained by a convex combination of the two one-sided fluxes. Construction of one-sided fluxes requires introducing the so-called harmonic averaging points as auxiliary points. While the nonlinear FVM can be applied to derive the flux for matrix-matrix connections in a straightforward way, difficulties arise for fracture-fracture connections because of the presence of fracture intersections. Therefore, to construct the one-sided fluxes for fracture-fracture connections, we first present a novel generalization of the concept of harmonic averaging point so that auxiliary points can be calculated at fracture intersections. Unique nonlinear fluxes are then derived for fracture-fracture connections and fracture intersections. Results of the numerical examples demonstrate that the linear TPFA coupling of matrix and fracture seems to be adequate even for relatively strong anisotropy on a non-K-orthogonal grid, and the new DFM model can accurately capture the permeability anisotropy effect inside the fracture planes as well as the permeability anisotropy in the matrix domain compared with the equidimensional models in which the fractures are gridded explicitly. Finally, the DFM model is applied successfully to deal with complex fracture networks embedded in a heterogeneous matrix domain or fracture network with challenging geometric features.

scholarly journals Local quasigeoid modelling in Slovakia using the finite volume method on the discretized Earth's topography

2020 ◽  
Vol 50 (3) ◽  
pp. 287-302
Author(s):  
Róbert ČUNDERLÍK ◽  
Matej MEDĽA ◽  
Karol MIKULA
Keyword(s):  
Numerical Solution ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Large Scale ◽  
Horizontal Resolution ◽  
Geopotential Model ◽  
Computational Domain ◽  
Disturbing Potential ◽  
Volume Method ◽  
Upper Boundary

The paper presents local quasigeoid modelling in Slovakia using the finite volume method (FVM). FVM is used to solve numerically the fixed gravimetric boundary value problem (FGBVP) on a 3D unstructured mesh created above the real Earth's surface. Terrestrial gravimetric measurements as input data represent the oblique derivative boundary conditions on the Earth's topography. To handle such oblique derivative problem, its tangential components are considered as surface advection terms regularized by a surface diffusion. The FVM numerical solution is fixed to the GOCE-based satellite-only geopotential model on the upper boundary at the altitude of 230 km. The horizontal resolution of the 3D computational domain is 0.002 × 0.002 deg and its discretization in the radial direction is changing with altitude. The created unstructured 3D mesh of finite volumes consists of 454,577,577 unknowns. The FVM numerical solution of FGBVP on such a detailed mesh leads to large-scale parallel computations requiring 245 GB of internal memory. It results in the disturbing potential obtained in the whole 3D computational domain. Its values on the discretized Earth's surface are transformed into the local quasigeoid model that is tested at 404 GNSS/levelling benchmarks. The standard deviation of residuals is 2.8 cm and decreases to 2.6 cm after removing 9 identified outliers. It indicates high accuracy of the obtained FVM-based local quasigeoid model in Slovakia.

Higher Resolution Hybrid-Upwind Spectral Finite-Volume Methods, for Flow in Porous and Fractured Media on Unstructured Grids

2021 ◽  
Author(s):  
Yawei Xie ◽  
Michael G. Edwards
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Unstructured Grids ◽  
Concentration Field ◽  
Convective Transport ◽  
High Order ◽  
Spectral Volume ◽  
Flux Approximation ◽  
Triangular Cell ◽  
Volume Method

Abstract A novel higher resolution spectral volume method coupled with a control-volume distributed multi-Point flux approximation (CVD-MPFA) is presented on unstructured triangular grids for subsurface reservoir simulation. The flow equations involve an essentially hyperbolic convection equation coupled with an elliptic pressure equation resulting from Darcy’s law together with mass conservation. The spectral volume (SV) method is a locally conservative, efficient high-order finite volume method for convective flow. In 2D geometry, the triangular cell is subdivided into sub-cells, and the average state variables in the sub-cells are used to reconstruct a high-order polynomial in the triangular cell. The focus here is on an efficient strategy for reconstruction of both a higher resolution approximation of the convective transport flux and Darcy-flux approximation on sub-cell interfaces, which is also coupled with a discrete fracture model. The strategy involves coupling of the SV method and reconstructed CVD-MPFA fluxes at the faces of the spectral volume, to obtain an efficient finer scale higher resolution finite-volume method which solves for both the saturation and pressure. A limiting procedure based on a Barth-Jespersen type limiter is used to prevent non-physical oscillations on unstructured grids. The fine scale saturation/concentration field is then updated via the reconstructed finite volume approximation over the sub-cell control-volumes. Performance comparisons are presented for two phase flow problems on 2D unstructured meshes including fractures. The results demonstrate that the spectral-volume method achieves further enhanced resolution of flow and fronts in addition to that of achieved by the standard higher resolution method over first order upwind, while improving upon efficiency.

An Explicit Modeling Approach for Simulating Fluid-Structure Interaction Problems With Immersed-Boundary Finite-Volume Method

2019 ◽  
Author(s):  
Yanbo Huang ◽  
Shanshan Li ◽  
Zhenhai Pan
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Numerical Experiments ◽  
Fluid Structure Interaction ◽  
Immersed Boundary ◽  
Computational Domain ◽  
Fluid Structure ◽  
Structure Interaction ◽  
Modeling Approach ◽  
Volume Method

Abstract Fluid-structure interaction (FSI) is an important fundamental problem with wide scientific and engineering applications. The immersed boundary method has proved to be an effective way to model the interaction between a moving solid and its surrounding fluid. In this study, a novel modeling approach based on the coupled immersed-boundary and finite-volume method is proposed to simulate fluid-structure interaction problems. With this approach, the whole computational domain is treated as fluid and discretized by only one set of Eulerian grids. The computational domain is divided into solid parts and fluid parts. A goal velocity is locally determined in each cell inside the solid part. At the same time, the hydrodynamic force exerted on the solid structure is calculated by integrating along the faces between the solid cells and fluid cells. In this way, the interaction between the solid and fluid is solved explicitly and the costly information transfer between Lagranian grids and Eulerian grids is avoided. The interface is sharply restricted into one single grid width throughout the iterations. The proposed modeling approach is validated by conducting several classic numerical experiments, including flow past static and freely rotatable square cylinders, and sedimentation of an ellipsoid in finite space. Throughout the three numerical experiments, satisfying agreements with literatures have been obtained, which demonstrate that the proposed modeling approach is accurate and robust for simulating FSI problems.

Calculation of the Unsteady Gas Flow Around a Projectile Moving Through a Gun Barrel

2003 ◽  
Author(s):  
Valery Ponyavin ◽  
Roald Akberov ◽  
Yitung Chen ◽  
Hsuan-Tsung Hsieh ◽  
Darrell W. Pepper
Keyword(s):  
Shock Waves ◽  
Flow Pattern ◽  
Finite Volume Method ◽  
Finite Volume ◽  
Gas Flow ◽  
Computational Domain ◽  
Gun Barrel ◽  
Volume Method ◽  
Unsteady Gas Flow ◽  
Velocity Pressure

The calculation of gas flow during the motion of a projectile in the gun barrel is a complicated computational task due of the presence of numerous factors, such as nonisothermicity, turbulence, changes in the shape of the computational domain with time, etc. In this study, an attempt to calculate the characteristics of gas flow around a projectile during the motion of the projectile in the gun barrel is undertaken. The flow is considered axisymmetrical, nonstationary, nonisothermal, compressible, and turbulent. For calculating the flow around the projectile, the finite volume method was employed. During the motion of the projectile, the flow pattern behind it changed from subsonic to supersonic. The results of the calculations are represented in figures depicting the flow at different moments of time. The figures show the fields of velocity, pressure and density, as well as the appearance of shock waves inside the gun barrel at subsonic and supersonic speeds.

A Zonal Approach for Navier-Stokes Computations of Compressible Cascade Flow Fields Using a TVD Finite Volume Method

1990 ◽  
Author(s):  
M. Furukawa ◽  
M. Yamasaki ◽  
M. Inoue
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Stokes Equations ◽  
Viscous Flows ◽  
Navier Stokes ◽  
Tvd Scheme ◽  
Computational Domain ◽  
Numerical Fluxes ◽  
Volume Method ◽  
Zonal Boundary

A new zonal approach for computation of compressible viscous flows in cascades has been developed. The two-dimensional, Reynolds-averaged Navier-Stokes equations are discretized spatially by a cell-centered finite volume formulation. In order to make the present approach robust, the inviscid fluxes at cell interfaces are evaluated using a highly accurate TVD scheme based on the MUSCL-type approach with the Roe’s approximate Riemann solver. The viscous fluxes are determined in a central differencing manner. To simplify the grid generation, a composite zonal grid system is adopted, in which the computational domain is divided into non-overlapping zones, and structured grids are generated independently in each zone. The zonal boundary between two zones is uniquely defined by cell interfaces of one zone, which ensures the uniqueness of the zonal boundary. The communication from one zone to the other is accomplished by numerical fluxes across the zonal boundary. It should be noted that the complete conservation of the numerical fluxes across the zonal boundary can be satisfied by directly evaluating the numerical fluxes using the finite volume method and by ensuring the uniqueness of the zonal boundary. In order to demonstrate the versatility of the present zonal approach, numerical examples are presented for viscous flows through a transonic turbine cascade.

Computation of the Spectral Signature Behind a Jet Engine Using the Finite Volume Method

2000 ◽  
Author(s):  
Thomas Badinand ◽  
Heino Tamvel ◽  
Torsten H. Fransson
Keyword(s):  
Finite Volume Method ◽  
Finite Volume ◽  
Wave Number ◽  
Spectral Signature ◽  
Computational Domain ◽  
Jet Engine ◽  
Infrared Signature ◽  
Practical Tool ◽  
Sensibility Analysis ◽  
Volume Method

Abstract A method is developed to compute the infrared signature behind a jet engine. The radiative transfer equation is solved with the Finite Volume Method (FVM) based on a double discretization of the spatial and the directional domain. Then, by solving step-by-step for different wave numbers for all directions, the value of the intensity received by a point placed at infinity looking at the computational domain with a defined angle and at a defined wave number is obtained. The resulting values of the intensity for a jet engine plume case compared very well with results from a validated ray-tracing model. A sensibility analysis has been carried out to assess the influence of the spatial and directional mesh, as well as the composition of the gas mixture on the results. The method appeared to be a very powerful and practical tool to study the spectral radiative signature created by a flow with arbitrary geometry.

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