Stabilized Methods for Compressible Flows

This article reviews 25 years of research of the authors and their collaborators on stabilized methods for compressible flow computations. An historical perspective is adopted to document the main advances from the initial developments to modern approaches.     

Effective fracture network permeability of geothermal reservoirs

This paper presents a new, simple, computationally efficient and practical method to accurately calculate effective fracture network permeabilities (EFNPs) for fracture dominated reservoirs. A set of fracture patterns from the outcrops of geothermal reservoirs in southwestern Turkey were chosen and their EFNP values were predicted using the new method; the computed permeabilities are comparable to those obtained with a commercial software package. The proposed method is based on 2-D fracture outcrop data, and is therefore limited to 2-D fracture networks.     

Interface projection techniques for fluid–structure interaction modeling with moving-mesh methods

The stabilized space–time fluid–structure interaction (SSTFSI) technique developed by the Team for Advanced Flow Simulation and Modeling (T★AFSM) was applied to a number of 3D examples, including arterial fluid mechanics and parachute aerodynamics. Here we focus on the interface projection techniques that were developed as supplementary methods targeting the computational challenges associated with the geometric complexities of the fluid–structure interface. Although these supplementary techniques were developed in conjunction with the SSTFSI method and in the context of air–fabric interactions, they can also be used in conjunction with other moving-mesh methods, such as the Arbitrary Lagrangian–Eulerian (ALE) method, and in the context of other classes of FSI applications. The supplementary techniques currently consist of using split nodal values for pressure at the edges of the fabric and incompatible meshes at the air–fabric interfaces, the FSI Geometric Smoothing Technique (FSI-GST), and the Homogenized Modeling of Geometric Porosity (HMGP). Using split nodal values for pressure at the edges and incompatible meshes at the interfaces stabilizes the structural response at the edges of the membrane used in modeling the fabric. With the FSI-GST, the fluid mechanics mesh is sheltered from the consequences of the geometric complexity of the structure. With the HMGP, we bypass the intractable complexities of the geometric porosity by approximating it with an “equivalent”, locally-varying fabric porosity. As test cases demonstrating how the interface projection techniques work, we compute the air–fabric interactions of windsocks, sails and ringsail parachutes.     

Analysis of counter-current gas–water capillary imbibition transfer at different temperatures

Gas water counter-current matrix–fracture interaction due to capillary forces was studied. The focus was on the rate of capillary imbibition and the development of residual gas phase under low (20 °C) and high temperatures (90 °C). Berea sandstone and Indiana limestone samples with different shape factors were obtained by cutting the plugs 1, 2.5, and 5 cm in diameter and 2.5, 5, and 10 cm in length. All sides were coated with epoxy except one end. Static imbibition experiments were conducted on vertically and horizontally situated samples where the matrix–fracture interaction took place upward and lateral directions, respectively. The effects of the matrix shape factor, wettability, surface tension, and core position on the recovery rate and ultimate recovery were investigated.The experimental scheme followed was useful in identification of the development of residual gas saturation for fully counter-current matrix–fracture interaction. We investigated and clarified to what degrees the rock/fluid properties (wettability and matrix shape factor) and existing conditions (temperature, causing lowered IFT and brine viscosity, and gravity) become effective on the residual gas saturation. It was observed that the residual gas saturation is sensitive to the matrix shape factor. The effect of surface tension on the recovery rate and ultimate recovery was also critical. The vertical cases yielded different recovery rates and ultimate recoveries with increasing temperature. Lower residual gas saturation with increasing temperature was obtained only for large diameters. That was attributed to the reduction in surface tension.Finally, critical matrix and fluid properties were correlated to the residual gas saturation and different dimensionless groups were tested for scaling.     

A highly novel dinickel complex: A hydrogen-bonded anti-skew carboxylate bridge and a 2D supramolecular structure

Reaction of the tridentate Schiff base ligands obtained from 2,4-dihydroxybenzaldehyde and either l-isoleucine or l-tert-leucine with Ni(NO₃)₂ in methanol/water solution in the presence of base afforded dinickel complexes. The crystal structure of the product derived from l-tert-leucine has been determined by X-ray crystallography. The octahedrally coordinated two Ni centers were found to be bridged by a single carboxylate group in an extremely unusual non-planar fashion. A 2D supramolecular structure, constructed by infinite hydrogen-bonded complex sheets parallel to the ab-plane of the unit cell, arises from intermolecular O–H?O hydrogen bonds.     

Thermal expansion of self-consolidating normal and lightweight aggregate concrete at elevated temperature

In this study, the effects of aggregate type on the coefficient of thermal expansion of self-consolidating concrete produced with normal (SCC) and lightweight aggregate (SCLC) at elevated temperature were investigated. In experiments, two aggregate types, crushed limestone and pumice, were used. Different combinations of water/powder ratio and superplasticizer dosage levels were prepared for the SCC and SCLC mixtures. The total powder content (cement and mineral additives) was constant in the experiments. Thermal test was performed to accurately characterize the coefficient of thermal expansion (CTE) of SCC and SCLC aged 28 days using the dilatometer. The CTEs of SCC and SCLC were defined by measuring the linear change in length of concrete specimens subjected to a range of temperatures. Test temperatures were varied from 20 to 1000 °C at a heating rate of 5 °C/min. The results, in general, showed that SCC has higher CTE than normal weight concrete and that lightweight aggregate reduced the CTE of SCC due to their porous structure. The aggregate type has significant influence on the thermal expansion of SCC.     

Enhanced-discretization Selective Stabilization Procedure (EDSSP)

The enhanced-discretization selective stabilization procedure (EDSSP) provides a multiscale framework for applying numerical stabilization selectively at different scales. The EDSSP is based on the enhanced-discretization, multiscale function space concept underlying the enhanced- discretization successive update method (EDSUM). The EDSUM is a multi-level iteration method designed for computation of the flow behavior at small scales. It has a built-in mechanism for transferring flow information between the large and small scales in a fashion consistent with the discretizations resulting from the underlying stabilized formulations. This is accomplished without assuming that the small-scale trial or test functions vanish at the borders between the neighboring large-scale elements of the enhanced-discretization zones. This facilitates unrestricted movement of small-scale flow patterns from one large-scale element to another without any constraints at the border between the two elements. The enhanced-discretization concept underlying the EDSUM can also facilitate using different stabilizations for equations or unknowns corresponding to different scales. In this paper we propose a version of the EDSSP where the SUPG and PSPG stabilizations are used for unknowns corresponding to both the large and small scales but the discontinuity-capturing stabilizations are used for unknowns corresponding to only the small scales. We also propose a version where a linear discontinuity-capturing is used for the small-scale unknowns and a nonlinear discontinuity-capturing is used for the large-scale unknowns. We evaluate the performances of these versions of the EDSSP with test problems governed by the advection–diffusion equations.     

Effect of Welding Parameters on Tensile Properties and Fatigue Behavior of Friction Stir Welded 2014-T6 Aluminum Alloy

The present work describes the effect of welding parameters on the tensile properties and fatigue behaviour of 2014-T6 aluminum alloy joints produced by friction stir welding (FSW). Characterization of the samples has been carried out by means of microstructure, microhardness, tensile properties and fatigue behaviors. The hardness in the softened weld region decreases with decreasing the welding speed. Irrespective of the tool rotation speeds, the best tensile and fatigue properties were obtained in the joints with the welding speed of 80 mm/min. The joint welded with a rotating speed of 1520 rpm at 80 mm/min has given a highest tensile and fatigue properties. The fatigue behaviors of the joints are almost consistent with the tensile properties, especially elongations. Higher ductility in FSW joints made the material less sensitive to fatigue. The location of tensile fractures of the joints is dependent on the welding parameters. On the other hand, the fatigue fracture locations change depending on the welding parameters and stress range. In addition, a considerable correlation could not be established in between heat indexes and mechanical properties of FSW 2014-T6 joints under the investigated welding parameters.     

Computation of Inviscid Supersonic Flows Around Cylinders and Spheres with the SUPG Formulation and YZβ Shock-Capturing

Numerical experiments with inviscid supersonic flows around cylinders and spheres are carried out to evaluate the stabilization and shock-capturing parameters introduced recently for the Streamline–Upwind/Petrov–Galerkin (SUPG) formulation of compressible flows based on conservation variables. The tests with the cylinders are carried out for both structured and unstructured meshes. The new shock-capturing parameters, which we call “YZβ Shock-Capturing”, are compared to earlier SUPG parameters derived based on the entropy variables. In addition to being much simpler, the new shock-capturing parameters yield better shock quality in the test computations, with more substantial improvements seen for unstructured meshes with triangular and tetrahedral elements. Furthermore, the results obtained with YZβ Shock-Capturing compare very favorably to those obtained with the well established OVERFLOW code     

Compressible Flow SUPG Stabilization Parameters Computed from Degree-of-freedom Submatrices

We present, for the SUPG formulation of inviscid compressible flows, stabilization parameters defined based on the degree-of-freedom submatrices of the element-level matrices. With 2D steady-state test problems involving supersonic flows and shocks, we compare these stabilization parameters with the ones defined based on the full element-level matrices. We also compare them to the stabilization parameters introduced in the earlier development stages of the SUPG formulation of compressible flows. In all cases the formulation includes a shock-capturing term involving a shock-capturing parameter. We investigate the difference between updating the stabilization and shock-capturing parameters at the end of every time step and at the end of every nonlinear iteration within a time step. The formulation includes, as an option, an algorithmic feature that is based on freezing the shock-capturing parameter at its current value when a convergence stagnation is detected.