Abstract: A Hybrid Embedded Fracture (HEF) model was developed to reduce various computational costs while maintaining physical accuracy (Amir and Sun, 2016). HEF splits the computations into fine scale and coarse scale. Fine scale solves analytically for the matrix-fracture flux exchange parameter. Coarse scale solves for the properties of the entire system. In literature, fractures were assumed to be either vertical or horizontal for simplification (Warren and Root, 1963). Matrix-fracture flux exchange parameter was given few equations built on that assumption (Kazemi, 1968; Lemonnier and Bourbiaux, 2010). However, such simplified cases do not apply directly for actual random fracture shapes, directions, orientations …etc. This paper shows that the HEF fine scale analytic solution (Amir and Sun, 2016) generates the flux exchange parameter found in literature for vertical and horizontal fracture cases. For other fracture cases, the flux exchange parameter changes according to the angle, slop, direction, … etc. This conclusion rises from the analysis of both: the Discrete Fracture Network (DFN) and the HEF schemes. The behavior of both schemes is analyzed with exactly similar fracture conditions and the results are shown and discussed. Then, a generalization is illustrated for any slightly compressible single-phase fluid within fractured porous media and its results are discussed.

Abstract: To compute flows around objects with complicated motion like the intermeshing rotors, the unstructured moving grid finite volume method was developed. Computational elements are added and eliminated according to motion of rotors, to keep the computation domain around rotors which mutually reverse. Also, the geometric conservation law is satisfied in the method, using four dimensional space time unified domain for control volume. Using the method, accurate computation is carried out without interpolation of physical quantities. Applying to a flow around a sphere, computation procedure was established with introduction of concept of a hierarchical grid distinction. Then, the results of application to the flow around intermeshing rotors showed efficacy of the method. The results also showed applicability of the method to compute flows around any complicated motion.

Abstract: We extend a regularization based numerical method for a highly degenerate partial differential equation that describes biofilm growth to systems of PDEs describing biofilms with several particulate substances. The example for which we develop the method is a quorum sensing biofilm which consists of donwn- and up-regulated biomass fractions. We carry out computational studies to assess the effect of the regularization parameter, a grid refinement study and report briefly on parallel performance of our code under OpenMP on desktop workstations.

Abstract: To improve the research methods in petroleum industry, we develop a fast algorithm to simulate droplet motions in oil and water two phase flow, using phase field model to describe the phase distribution in the flow process. An efficient partial difference equation solver—Shift-Matrix method is applied here, to speed up the calculation coding in high-level language, i.e. Matlab and R. An analytical solution of order parameter is derived, to define the initial condition of phase distribution. The upwind scheme is applied in our algorithm, to make it energy decay stable, which results in the fast speed of calculation. To make it more clear and understandable, we provide the specific code for forming the coefficient matrix used in Shift-Matrix Method. Our algorithm is compared with other methods in different scales, including Front Tracking and VOSET method in macroscopic and LBM method using RK model in mesoscopic scale. In addition, we compare the result of droplet motion under gravity using our algorithm with the empirical formula common used in industry. The result proves the high efficiency and robustness of our algorithm and it’s then used to simulate the motions of multiple droplets under gravity and cross-direction forces, which is more practical in industry and can be extended to wider application.

Abstract: Centrifugal compressors are one of the most commonly used equipments powering the long distance natural gas pipeline. In this paper, a similarity conversion method of centrifugal natural gas compressors based on predictor-corrector was proposed. In other words, we used one similarity conversion to predict the key parameter and the other was used as the correction. Compared with the field test data, we found the error of the predicted outlet pressure of the compressor was controlled at about 2% and the outlet temperature fluctuated within 2℃, which could satisfy the engineering application requirements.

Abstract: In this paper, we first present the THex algorithm that refines a tetrahedral mesh into a hexahedral mesh. Strategies for efficient implementation of the THex algorithm are discussed. Then we present the lowest order weak Galerkin (WG) $ (Q_0,Q_0;RT_{[0]}) $ finite element method for solving the Darcy equation on general hexahedral meshes. This simple solver uses constant pressure unknowns inside hexahedra and on faces but specifies the discrete weak gradients of these basis functions in local Raviart-Thomas $ RT_{[0]} $ spaces. The solver has easy implementation, is locally mass-conservative, and produces continuous normal fluxes, regardless of hexahedral mesh quality. When the mesh is asymptotically parallelopiped, this Darcy solver exhibits optimal order convergence in pressure, velocity, and flux, as demonstrated by numerical results.

Abstract: Aiming at the development of a practically parallelizable algorithm for the simulation of fluid-structure interaction (FSI) problems in the future, in this paper a type of elliptic interface problem with jump coefficients is chosen to begin with and is reformulated to a mixture of elliptic/mixed elliptic interface problem which is analogous to a steady state FSI problem to some extent. A mixture of standard- and mixed finite element method is developed for the reformulation of the elliptic interface problem, and its well-posedness and convergence are studied by proving the inf-sup condition of a total bilinear form. With the body-fitted meshes and a strongly coupled alternating iteration scheme, numerical experiments are carried out for an elliptic interface problem with an immersed interface for different jump ratios, and the obtained numerical results confirm our convergence theorem.

Abstract: In this paper, stabilized continuous finite element methods are analyzed for numerically solving the flux which may be a non $H^1$ solution. Coercivity and error estimates are established. Numerical experiments are performed to illustrate these methods.

Abstract: In the Cartesian grid approach, the immersed boundary method (IBM) is well used to handle the boundary of an object with complicated shape on the Cartesian grid. However, the conventional IBM generates the unphysical pressure oscillations near the boundary because of the pressure jump between inside and outside of the boundary. The IBM considering pressure condition was proposed in order to remove the pressure oscillations by solving the governing equations considering the pressure condition on the boundary. In this method, there are two ways of the handling the pressure on the boundary in the Poisson solver. In this paper, the effect of removing the pressure oscillations by the IBM considering the pressure condition is investigated. And, the influence by the difference in the handling of the pressure on the boundary in the Poisson solver is investigated. In the numerical simulations of incompressible flow around a 2D circular cylinder, the present IBM indicate a greate effect of removing the pressure oscillations. And, it do not occur difference of the result by the difference of the handling the pressure on the boundary in the Poisson solver. Therefore, it is possible to select a method with less computational amount in the Poisson solver without degrading the quality of the result. It is concluded that the present IBM is very promising as improved method in order to remove the pressure oscillations in the conventional IBM.

Abstract: Many fluid flow problems involving turbulence, shocks, and material interfaces create a common issue that we call $k_\infty$ irregularity. The non-linear advection term in the governing equations for all of these problems keep generating higher wave modes as $k$ goes to infinity. In this work, we present an inviscid regularization technique, called observable regularization, for the simulation of two-phase compressible flow. In this technique, we use observable divergence theorem to derive an observable equation for tracking material interface (volume fraction). Using a couple of one-dimensional test cases, first we show that this method preserves pressure equilibrium at material interface, then we compare our results to exact Euler solutions. At the end we demonstrate a two-dimensional simulation of shock-bubble interaction showing good agreement with available experimental data from literature.

Abstract: The kidneys are vital organs that contribute to the maintenance of homeostasis in our body. They fulfill functions such as electrolyte control, blood filtration and initiation of red blood cell production in response to hypoxia, a state characterized by deficiency of oxygen (O2 ) in the renal tissue. A normal human kidney contains between 0.8 to 1.5 million functional units called nephrons. Renal tubules along the nephrons are responsible for the reabsorption of various solutes including sodium ions (Na+ ), a process that requires large amounts of O2. Physiological and pathophysiological variation in Na+ transport can alter O2 consumption, leading to changes in tissue oxygenation. We have developed a one-dimensional (1D) mathematical model for the computation of Na+ reabsorption and corresponding O2 consumption along a nephron, which is parameterized using published data obtained from a rat kidney. Our computations demonstrate that per kidney 8μ-moles of O2 are consumed per minute for the reabsorption of 125μ-moles of Na+ , which is in agreement with previously published results. The model also predicts that changes in arterial pressure adversely impact the efficiency of O2 consumption in the nephron. The model is further being extended to account for anatomically realistic renal vasculature obtained from synchrotron X-ray phase contrast micro computed tomography, with the final goal of determining O2 distribution in the whole kidney.

Abstract: CFD (Computational Fluids Dynamic) is an important branch of fluid dynamics. It applies various kinds of discrete mathematical method to analyze and simulate problems in fluid mechanics with the use of computer. During the computation, huge computational tasks on a single CPU often makes it very inefficient to get the result, so there is an increasing number of application of parallel computation in CFD. With more powerful computing capability and lower price, GPU (Graphic Processing Unit) has become a better solution for parallel computing than CPU in recent years. In this paper, we implemented the HSMAC and SIMPLE algorithms on GPU. For the simulation of 2D lid-driven cavity flow, the GPU version could get a speedup up to 58x and 21x respectively with double precision, and 78x and 32x with single precision, compared to the sequential CPU version. It demonstrates a good prospects of GPU acceleration of CFD algorithms.

Abstract: Numerical modeling of gas and liquid flows and, in particular, multiphase mediums, is a promising direction of scientific investigations and development of industrial apparatus. Experimental approach in the field of multiphase flows is not always capable of obtaining required information about the flow structure due to the excessive amount of physical phenomena involved. Numerical simulations of real flows with inclusion of all processes and phenomena or on real-scale geometries are very resource-demanding and are not feasible on stand-alone personal working stations. Thus, applying parallelization techniques at the existing solution algorithms with the means of OpenMP library alongside with supercomputer technologies can reduce computational time and can help with simulations of complex flows on the systems with shared memory. The study presents the description of the previously developed mathematical model of polydisperse multiphase flows, numerical algorithm for the solution of governed equations of the model and description of the numerical method. Simulations by the means of the proposed algorithm were carried out for the case of polydisperse bubbly flow inside water-filled rectangular column. Results presented in the paper, which are obtained during numerical experiments carried out on the “SC Politechnichesky”, comprise of the obtained flow field and bubble distributions and of the dependencies of program working time on the amount of threads and model parameters.

Abstract: In this work, a hybrid particle-grid method coupled with a penalization technique is introduced in order to compute Direct Numerical Simulations in three dimensions. The method is validated with the litterature for the flow past a sphere and a hemisphere. The approach is extented to solid-porous-fluid media and applied to passive flow control for the hemisphere using porous coatings.

Abstract: This paper presents a numerical study of the gravity-driven motion of single bubbles and bubble swarms through a vertical channel, using High Performance Computing (HPC) and Direct Numerical Simulation (DNS) of the Navier-Stokes equations. A systematic study of the wall effect on the motion of single deformable bubbles is carried out for confinement ratios CR={2,4,6}. Then, the rising motion of a swarm of deformable bubbles in a vertical channel is researched, for void fractions alpha={8.33%,12.5%}. These simulations are carried out in the framework of a novel multiple marker interface capturing approach, where each bubble is represented by a conservative level-set function. This method has the ability to avoid the numerical and potentially unphysical coalescence of the bubbles, allowing for the collision of the fluid particles as well as long time simulations of bubbly flows. Present simulations are performed in a periodic vertical domain discretized by 2e6 control volumes (CVs) up to 21e6 CVs, distributed in 128 up to 2048 processors. Collective and individual behaviour of the bubbles are characterized and compared against previous results from the literature.

Abstract: This work deals with an extension of the Path Tubes method for the solution of the timedependent Navier-Stokes equations for an incompressible Newtonian fluid. The resulting technique Departing from a physically intuitive methodology based on the theoretical basis of the mechanics of continuous media, a robust numerical technique is obtained. This version of the Path Tubes method draws on a semi-Lagrangian time-discretization employs the Reynolds’ transport theorem, and a localization approach, to establish an implicit semi-Lagrangian algorithm that allows the use of classical schemes for spatial discretization, such as central-difference formulas, without the need to use upwind techniques, or high-order corrections for time derivatives. Some of the extensive numerical tests are shown herein, in particular for Reynolds’ numbers typical of advection dominated flows. The tests are shown to be accurate and perform well even for coarse grids.

Abstract: A new second-order numerical scheme based on an operator splitting is proposed for the Godunov-Peshkov-Romenski model of continuum mechanics. The homogeneous part of the system is solved with a finite volume method based on a WENO reconstruction, and the temporal ODEs are solved using some analytic results presented here. Whilst it is not possible to attain arbitrary-order accuracy with this scheme (as with ADER-WENO schemes used previously), the attainable order of accuracy is often sufficient, and solutions are computationally cheap when compared with other available schemes. The new scheme is compared with a second-order ADER-WENO scheme for various test cases, and a convergence study is undertaken to demonstrate its order of accuracy.