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The accelerated pace of change in the global economy and capital markets along with the complexity of transactions and financial reporting that involve applying fair value measurements (FVM) is a major third-party user concern. The 2008 financial crisis highlighted risks that investors are exposed to when making FVM-related capital allocations. Accounting estimates often involve subjective assumptions and measurement uncertainty, increasing potential management bias (Choudhary, 2011; Ramanna & Watts, 2012). FVMs are of critical importance to the reliability of the financial statements. Therefore, the purpose of this chapter is to inform educators of the possible need to evaluate their curriculum as to coverage of FVM topics. The support for this evaluation is based on our attempt to: (1) evaluate the extent of reported FVM-related deficiencies with reference to regulatory bodies’ findings of significant deficiencies in FVM; (2) examine the use of FVM specialists; (3) determine if colleges and universities are keeping pace with FVM demands; (4) list the Uniform CPA Examination Blueprint FVM testing areas; and (5) provide curricular FVM topic recommendations.

Selective laser melting (SLM) is a major additive manufacturing (AM) process in which laser beams are used as the heat source to melt and deposit metals in a layerwise fashion to enable the construction of components of arbitrary complexity. The purpose of this paper is to develop a framework for accurate and fast prediction of the temperature distribution during the SLM process.

A fast computation tool is proposed for thermal analysis of the SLM process. It is based on the finite volume method (FVM) and the quiet element method to allow the development of customized functionalities at the source level. The results obtained from the proposed FVM approach are compared against those obtained from the finite element method (FEM) using a well-established commercial software, in terms of accuracy and efficiency.

The results show that for simulating the SLM deposition of a cubic block with 81,000, 189,000 and 297,000 cells, the computation takes about 767, 3,041 and 7,054 min, respectively, with the FEM approach; while 174, 679 and 1,630 min with the FVM code. This represents a speedup of around 4.4x. Meanwhile, the average temperature difference between the two is below 6%, indicating good agreement between them.

The thermal field for the multi-track and multi-layer SLM process is for the first time computed by the FVM approach. This pioneering work on comparing FVM and FEM for SLM applications implies that a fast and simple computing tool for thermal analysis of the SLM process is within the reach, and it delivers comparable accuracy with significantly higher computational efficiency. The research results lay the foundation for a potentially cost-effective tool for investigating the fundamental microstructure evolution, and also optimizing the process parameters in the SLM process.

The paper aims to use the finite volume method widely used in computational fluid dynamics to avoid the serious remeshing and mesh distortion during aluminium profile extrusion processes simulation when using the finite element method. Block-structured grids are used to fit the complex domain of the extrusion. A finite volume method (FVM) model for aluminium extrusion numerical simulation using non-orthogonal structured grids was established.

The influences of the elements ' nonorthogonality on the governing equations discretization of the metal flow in aluminium extrusion processes were fully considered to ensure the simulation accuracy. Volume-of-fluid (VOF) scheme was used to catch the free surface of the unsteady flow. Rigid slip boundary condition was applied on non-orthogonal grids.

This paper involved a simulation of a typical aluminium extrusion process by the FVM scheme. By comparing the simulation by the FVM model established in this paper with the ones simulated by the finite element method (FEM) software Deform-3D and the corresponding experiments, the correctness and efficiency of the FVM model for aluminium alloy profile extrusion processes in this paper was proved.

This paper uses the FVM widely used in CFD to calculate the aluminium profile extrusion processes avoiding the remeshing and mesh distortion during aluminium profile extrusion processes simulation when using the finite element method. Block-structured grids with the advantage of simple data structure, small storage and high numerical efficiency are used to fit the complex domain of the extrusion.

The purpose of this paper is to find an efficient way by using finite volume method (FVM) to simulate the aluminum alloy profile extrusion processes.

By assuming isotropic conditions, the hot aluminum material is described as a non‐linear Newtonian fluid material. Semi‐implicit method for pressure‐linked equations algorithm is used to calculate the physical fields, and the dynamic viscosity is updated then. Volume of fluid method and moving grid method are also used for unsteady flow to catch the free surface of the material and the moving bound.

FVM model in this paper is an accurate and efficient method for the numerical simulation of aluminum profile extrusion processes. Compared with finite element method software, FVM model is both memory and CPU efficient.

Provide theoretical reference for sound extrusion process and die designs, which are the key factors to produce desirable products in industrial production.

The paper finds an efficient way to introduce the FVM in computational fluid dynamics field into the simulation of the steady and unsteady aluminum alloy profile extrusion processes. It provides a reference for people who are interested in FVM and extrusion processes.

The purpose of this study is to extend a novel numerical method proposed by the first author, known as the dual mesh control domain method (DMCDM), for the solution of linear differential equations to the solution of nonlinear heat transfer and like problems in one and two dimensions.

In the DMCDM, a mesh of finite elements is used for the approximation of the variables and another mesh of control domains for the satisfaction of the governing equation. Both meshes fully cover the domain but the nodes of the finite element mesh are inside the mesh of control domains. The salient feature of the DMCDM is that the concept of duality (i.e. cause and effect) is used to impose boundary conditions. The method possesses some desirable attributes of the finite element method (FEM) and the finite volume method (FVM).

Numerical results show that he DMCDM is more accurate than the FVM for the same meshes used. Also, the DMCDM does not require the use of any ad hoc approaches that are routinely used in the FVM.

To the best of the authors’ knowledge, the idea presented in this work is original and novel that exploits the best features of the best competing methods (FEM and FVM). The concept of duality is used to apply gradient and mixed boundary conditions that FVM and its variant do not.

Present study aims to extend the lattice Boltzmann method (LBM) to simulate radiation in geometries with curved boundaries, as the first step to simulate radiation in complex porous media. In recent years, researchers have increasingly explored the use of porous media to improve the heat transfer processes. The lattice Boltzmann method (LBM) is one of the most effective techniques for simulating heat transfer in such media. However, the application of the LBM to study radiation in complex geometries that contain curved boundaries, as found in many porous media, has been limited.

The numerical evaluation of the effect of the radiation-conduction parameter and extinction coefficient on temperature and incident radiation distributions demonstrates that the proposed LBM algorithm provides highly accurate results across all cases, compared to those found in the literature or those obtained using the finite volume method (FVM) with the discrete ordinates method (DOM) for radiative information.

For the case with a conduction-radiation parameter equal to 0.01, the maximum relative error is 1.9% in predicting temperature along vertical central line. The accuracy improves with an increase in the conduction-radiation parameter. Furthermore, the comparison between computational performances of two approaches reveals that the LBM-LBM approach performs significantly faster than the FVM-DOM solver.

The difficulty of radiative modeling in combined problems involving irregular boundaries has led to alternative approaches that generally increase the computational expense to obtain necessary radiative details. To address the limitations of existing methods, this study presents a new approach involving a coupled lattice Boltzmann and first-order blocked-off technique to efficiently model conductive-radiative heat transfer in complex geometries with participating media. This algorithm has been developed using the parallel lattice Boltzmann solver.

The purpose of this paper is to propose to simulate an arbitrary movement in electromagnetic problems by means of a 3D nonconforming finite volume method (NC-FVM). The moving part can be displaced according to the x, y and/or z direction.

The 3D nonconforming mesh technique coupled to the FVM is used to handle arbitrary displacement of moving parts. Accordingly, the whole problem domain is divided into two parts: moving part and fixed part. Both parts are meshed independently. By using a suitable connection between both fixed and moved meshes, the movement can be performed according to the three axes.

The TEAM Workshop Problem No. 23 is used to test the proposed method. The calculated values of the magnetic force applied to the permanent magnet for different positions of the magnet show the efficiency of the proposed method.

This paper introduces the NC-FVM to solve electromagnetic problems which contain moving parts. Here, the movement can be performed according to the three axes.

We report on the progress in the development and application of a coupled boundary element/finite volume method temperature‐forward/flux‐back algorithm developed to solve conjugate heat transfer arising in 3D film‐cooled turbine blades. We adopt a loosely coupled strategy where each set of field equations is solved to provide boundary conditions for the other. Iteration is carried out until interfacial continuity of temperature and heat flux is enforced. The NASA‐Glenn explicit finite volume Navier‐Stokes code Glenn‐HT is coupled to a 3D BEM steady‐state heat conduction solver. Results from a CHT simulation of a 3D film‐cooled blade section are compared with those obtained from the standard two temperature model, revealing that a significant difference in the level and distribution of metal temperatures is found between the two. Finally, current developments of an iterative strategy accommodating large numbers of unknowns by a domain decomposition approach is presented. An iterative scheme is developed along with a physically‐based initial guess and a coarse grid solution to provide a good starting point for the iteration. Results from a 3D simulation show the process that converges efficiently and offers substantial computational and storage savings.

Lattice Boltzmann method (LBM) has made great success in computational fluid dynamics, and this paper aims to establish an efficient simulation model for the polymer injection molding process using the LBM. The study aims to validate the capacity of the model for accurately predicting the injection molding process, to demonstrate the superior numerical efficiency in comparison with the current model based on the finite volume method (FVM).

The study adopts the stable multi-relaxation-time scheme of LBM to model the non-Newtonian polymer flow during the filling process. The volume of fluid method is naturally integrated to track the movement of the melt front. Additionally, a novel fractional-step thermal LBM is used to solve the convection-diffusion equation of the temperature field evolution, which is of high Peclet number. Through various simulation cases, the accuracy and stability of the present model are validated, and the higher numerical efficiency verified in comparison with the current FVM-based model.

The paper provides an efficient alternative to the current models in the simulation of polymer injection molding. Through the test cases, the model presented in this paper accurately predicts the filling process and successfully reproduces several characteristic phenomena of injection molding. Moreover, compared with the popular FVM-based models, the present model shows superior numerical efficiency, more fit for the future trend of parallel computing.

Limited by the authors’ hardware resources, the programs of the present model and the FVM-based model are run on parallel up to 12 threads, which is adequate for most simulations of polymer injection molding. Through the tests, the present model has demonstrated the better numerical efficiency, and it is recommended for the researcher to investigate the parallel performance on even larger-scale parallel computing, with more threads.

To the authors’ knowledge, it is for the first time that the lattice Boltzmann method is applied in the simulation of injection molding, and the proposed model does obviously better in numerical efficiency than the current popular FVM-based models.

The purpose of this paper is to propose modelling 3D eddy current non destructive testing (EC NDT) problems by the finite volume method (FVM). Furthermore, the movement of the probe coil is taken into account.

The nonconforming mesh technique is used to handle the displacement of the probe coil. Thus, the whole problem is divided into two parts; moving part (probe coil) and fixed part (specimen with crack), and then each part meshes independently. A computer code is built under Matlab program to generate 3D nonconforming mesh, to calculate magnetic and electric potentials and to evaluate the impedance change of the coil due to the presence of the crack.

The JSAEM No. 6 problem is used to test the proposed method. The calculated values of the impedance change of the probe coil due to the presence of crack, shows the efficiency of the developed software. A small difference is obtained between calculated values and measured values.

The paper introduces the FVM in solving EC NDT problems where the probe displacement is taken into account.