Non-conservative Method Research Articles

Correlation between thyroid imaging reporting and data system with histopathology in classification of thyroid nodules

Objective This study aims to evaluate the reliability of the ACR-thyroid imaging reporting and data system (TIRADS) classification system in predicting thyroid malignancy by using pathology diagnosis as the reference standard. Patients and methods This was a prospective study that was carried out at Alzahraa University Hospital. Records of patients with focal thyroid nodules on ultrasound for which ultrasound-guided core needle was performed and pathology results were available, from January 2019 to June 2019, were selected for review. Correlation of the American college of Radiology - thyroid imaging reporting and data system (ACR-TIRADS) classification with pathology results was assessed. Sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were calculated in a conservative and nonconservative method. The threshold for statistical performance was set at 0.05. Each sonographic feature was also compared with its pathology results. Results A total number of 20 patients with 51 nodules were eligible in the study; seven (13.7%) of 51 nodules were malignant. The sensitivity, specificity, positive predictive value, negative predictive value, and accuracy were 85.7, 97.7, 85.7, 97.7, and 96.1%, respectively. Conclusion The ACR-TIRADS classification is reliable in predicting thyroid malignancy. More evidence is nevertheless necessary for widespread adaptation and use.

A hybrid numerical model for multiphase fluid flow in a deformable porous medium

In this paper, a fully coupled finite volume-finite element model for a deforming porous medium interacting with the flow of two immiscible pore fluids is presented. The basic equations describing the system are derived based on the averaging theory. Applying the standard Galerkin finite element method to solve this system of partial differential equations does not conserve mass locally. A non-conservative method may cause some accuracy and stability problems. The control volume based finite element technique that satisfies local mass conservation of the flow equations can be an appropriate alternative. Full coupling of control volume based finite element and the standard finite element techniques to solve the multiphase flow and geomechanical equilibrium equations is the main goal of this paper. The accuracy and efficiency of the method are verified by studying several examples for which analytical or numerical solutions are available. The effect of mesh orientation is investigated by simulating a benchmark water-flooding problem. A representative example is also presented to demonstrate the capability of the model to simulate the behavior in heterogeneous porous media.

Runge–Kutta discontinuous Galerkin method with front tracking method for solving the compressible two-medium flow

The Runge–Kutta discontinuous Galerkin method together with the front tracking method for solving the compressible two-medium flow is presented. The fluid interface boundary condition is defined via a non-conservative method based on the real ghost fluid method. A Riemann problem is constructed in the normal direction of the interface, the corresponding Riemann solutions are used to determine the motion of the interface and obtain the ghost fluid states directly. Extensive numerical tests including the gas–gas and gas–liquid flows are provided to illustrate that the proposed methods possess the capability of enhancing the resolutions nearby the discontinuities in the single medium and material interfacial vicinities.

Speeding up Monte Carlo molecular simulation by a non-conservative early rejection scheme

Monte Carlo (MC) molecular simulation describes fluid systems with rich information, and it is capable of predicting many fluid properties of engineering interest. In general, it is more accurate and representative than equations of state. On the other hand, it requires much more computational effort and simulation time. For that purpose, several techniques have been developed in order to speed up MC molecular simulations while preserving their precision. In particular, early rejection schemes are capable of reducing computational cost by reaching the rejection decision for the undesired MC trials at an earlier stage in comparison to the conventional scheme. In a recent work, we have introduced a ‘conservative’ early rejection scheme as a method to accelerate MC simulations while producing exactly the same results as the conventional algorithm. In this paper, we introduce a ‘non-conservative’ early rejection scheme, which is much faster than the conservative scheme, yet it preserves the precision of the method. The proposed scheme is tested for systems of structureless Lennard-Jones particles in both canonical and NVT-Gibbs ensembles. Numerical experiments were conducted at several thermodynamic conditions for different number of particles. Results show that at certain thermodynamic conditions, the non-conservative method is capable of doubling the speed of the MC molecular simulations in both canonical and NVT-Gibbs ensembles.

Model falsification using set-valued observers for a class of discrete-time dynamic systems: a coprime factorization approach

This article introduces a new method for model falsification using set-valued observers, which can be applied to a class of discrete linear time-invariant dynamic systems with time-varying model uncertainties. In comparison with previous results, the main advantages of this approach are as follows: The computation of the convex hull of the set-valued estimates of the state can be avoided under certain circumstances; to guarantee convergence of the set-valued estimates of the state, the required number of previous steps is at most as large as the number of states of the nominal plant; and it provides a straightforward nonconservative method to falsify uncertain models of dynamic systems, including open-loop unstable plants. The results obtained are illustrated in simulation, emphasizing the advantages and shortcomings of the suggested method. Copyright © 2013 John Wiley & Sons, Ltd.

A control volume based finite element method for simulating incompressible two-phase flow in heterogeneous porous media and its application to reservoir engineering

Applying the standard Galerkin finite element method for solving flow problems in porous media encounters some difficulties such as numerical oscillation at the shock front and discontinuity of the velocity field on element faces. Discontinuity of velocity field leads this method not to conserve mass locally. Moreover, the accuracy and stability of a solution is highly affected by a non-conservative method. In this paper, a three dimensional control volume finite element method is developed for two-phase fluid flow simulation which overcomes the deficiency of the standard finite element method, and attains high-orders of accuracy at a reasonable computational cost. Moreover, this method is capable of handling heterogeneity in a very rational way. A fully implicit scheme is applied to temporal discretization of the governing equations to achieve an unconditionally stable solution. The accuracy and efficiency of the method are verified by simulating some waterflooding experiments. Some representative examples are presented to illustrate the capability of the method to simulate two-phase fluid flow in heterogeneous porous media.

Analysis on Stability and Ultimate Bearing Capacity of Steel Truss Arch Bridge

Based on the secondary development of ANSYS, a through-type steel truss arch bridge is modeled, and the most unfavorable position of live load for each concerning location of the bridge is determined by using the influence lines program self-developed with parametric language. Linear elastic stability analysis of the whole bridge is firstly conducted, and followed by calculating the ultimate bearing capacity of the bridge with the consideration of geometrical and material nonlinearity of structure. By analyzing the buckling modes and safety coefficients of two types of stability problems, and comparing the linear elastic and nonlinear stability analysis results, the first type stability analysis, as a non-conservative method, is found to be suitable for ideal structures; the second stability analysis is found to be completely different from the first stability analysis, with different buckling mode and lower stability coefficient. Therefore, it can be concluded that the ultimate carrying capacity of structures should be determined based on the second stability analysis.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part II: Two-Dimensional Applications

A time-derivative preconditioned system of equations suitable for the numerical simulation of multicomponent/multiphase inviscid flows at all speeds was described in Part I of this paper. The system was shown to be hyperbolic in time and remain well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. Application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces was shown to generate nonphysical pressure and velocity oscillations across the contact surface, which separates the fluid components. It was demonstrated using the one-dimensional Riemann problem that these oscillations may lead to stability problems when the interface separates fluids with large density ratios, such as water and air. The effect of which leads to the requirement of small physical time steps and slow subiteration convergence for the implicit time marching numerical method. Alternatively, the nonconservative and hybrid formulations developed by the present authors were shown to eliminate this nonphysical behavior. While the nonconservative method did not converge to the correct weak solution for flow containing shocks, the hybrid method was able to capture the physically correct entropy solution and converge to the exact solution of the Riemann problem as the grid is refined. In Part II of this paper, the conservative, nonconservative, and hybrid formulations described in Part I are implemented within a two-dimensional structured body-fitted overset grid solver, and a study of two unsteady flow applications is reported. In the first application, a multiphase cavitating flow around a NACA0015 hydrofoil contained in a channel is solved, and sensitivity to the cavitation number and the spatial order of accuracy of the discretization are discussed. Next, the interaction of a shock moving in air with a cylindrical bubble of another fluid is analyzed. In the first case, the cylindrical bubble is filled with helium gas, and both the conservative and hybrid approaches perform similarly. In the second case, the bubble is filled with water and the conservative method fails to maintain numerical stability. The performance of the hybrid method is shown to be unchanged when the gas is replaced with a liquid, demonstrating the robustness and accuracy of the hybrid approach.

Time-Derivative Preconditioning Methods for Multicomponent Flows—Part I: Riemann Problems

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid multicomponent and multiphase flows at all speeds is described. The system is shown to be hyperbolic in time and remains well conditioned in the incompressible limit, allowing time marching numerical methods to remain an efficient solution strategy. It is well known that the application of conservative numerical methods to multicomponent flows containing sharp fluid interfaces will generate nonphysical pressure and velocity oscillations across the component interface. These oscillations may lead to stability problems when the interface separates fluids with large density ratio, such as water and air. The effect of which may lead to the requirement of small physical time steps and slow subiteration convergence for implicit time marching numerical methods. At low speeds the use of nonconservative methods may be considered. In this paper a characteristic-based preconditioned nonconservative method is described. This method preserves pressure and velocity equilibrium across fluid interfaces, obtains density ratio independent stability and convergence, and remains well conditioned in the incompressible limit of the equations. To extend the method to transonic and supersonic flows containing shocks, a hybrid formulation is described, which combines a conservative preconditioned Roe method with the nonconservative preconditioned characteristic-based method. The hybrid method retains the pressure and velocity equilibrium at component interfaces and converges to the physically correct weak solution. To demonstrate the effectiveness of the nonconservative and hybrid approaches, a series of one-dimensional multicomponent Riemann problems is solved with each of the methods. The solutions are compared with the exact solution to the Riemann problem, and stability of the numerical methods are discussed.

Preconditioned methods for simulations of low speed compressible flows

A time-derivative preconditioned system of equations suitable for the numerical simulation of inviscid compressible flow at low speeds is formulated. The preconditioned system of equations are hyperbolic in time and remain well-conditioned in the incompressible limit. The preconditioning formulation is easily generalized to multicomponent/multiphase mixtures. When applying conservative methods to multicomponent flows with sharp fluid interfaces, nonphysical solution behavior is observed. This stimulated the authors to develop an alternative solution method based on the nonconservative form of the equations which does not generate the aforementioned nonphysical behavior. Before the results of the application of the nonconservative method to multicomponent flow problems is reported, the accuracy of the method on single component flows will be demonstrated. In this report a series of steady and unsteady inviscid flow problems are simulated using the nonconservative method and a well-known conservative scheme. It is demonstrated that the nonconservative method is both accurate and robust for smooth low speed flows, in comparison to its conservative counterpart.

제어체적 복사열정산을 위한 구분종좌표보간법의 오차 및 보정방안

The discrete ordinates interpolation method (DOIM) has shown good accuracy and versatile applicability for the radiation problems(¹, ²). The DOIM is a nonconservative method in that the intensity and temperature are computed only at grid points without considering control volumes. However, when the DOIM is used together with a finite volume algorithm such as SIMPLER(3), intensities at the control surfaces need to be calculated. For this reason, a 'quadratic' and a 'decoration' schemes are proposed and examined. They are applied to two kinds of radiation problem in one-dimensional geometries. In one problem, the intensity and temperature are calculated while the radiative heat source is given, and in the other, the intensity and the radiative heat source are computed with a given temperature field. The quadratic and the decoration schemes show very successful results. The quadratic scheme gives especially accurate results so that further decoration may not be needed. It is recommended that the quadratic and the decoration schemes may be used together, or, one of them may be applied for control volume radiative energy balance.

Moving-least-squares-particle hydrodynamics?I. Consistency and stability

The Smooth-Particle-Hydrodynamics (SPH) method is derived in a novel manner by means of a Galerkin approximation applied to the Lagrangian equations of continuum mechanics as in the finite-element method. This derivation is modified to replace the SPH interpolant with the Moving-Least-Squares (MLS) interpolant of Lancaster and Saulkaskas, and define a new particle volume which ensures thermodynamic compatibility. A variable-rank modification of the MLS interpolants which retains their desirable summation properties is introduced to remove the singularities that occur when divergent flow reduces the number of neighbours of a particle to less than the minimum required. A surprise benefit of the Galerkin SPH derivation is a theoretical justification of a common ad hoc technique for variable-h SPH. The new MLSPH method is conservative if an anti-symmetric quadrature rule for the stiffness matrix elements can be supplied. In this paper, a simple one-point collocation rule is used to retain similarity with SPH, leading to a non-conservative method. Several examples document how MLSPH renders dramatic improvements due to the linear consistency of its gradients on three canonical difficulties of the SPH method: spurious boundary effects, erroneous rates of strain and rotation and tension instability. Two of these examples are non-linear Lagrangian patch tests with analytic solutions with which MLSPH agrees almost exactly. The examples also show that MLSPH is not absolutely stable if the problems are run to very long times. A linear stability analysis explains both why it is more stable than SPH and not yet absolutely stable and an argument is made that for realistic dynamic problems MLSPH is stable enough. The notion of coherent particles, for which the numerical stability is identical to the physical stability, is introduced. The new method is easily retrofitted into a generic SPH code and some observations on performance are made. Copyright © 1999 John Wiley & Sons, Ltd.