Computational fluid dynamics (CFD) is one of the tools available for understanding and predicting the performance of thermal-fluids systems. This article qualitatively describes the basic principles of CFD. The numerical methods, such as geometry description and discretization, used to solve the CFD equations are discussed. The article also demonstrates the application of CFD to a few casting problems.

Designing of induction heating, or, generally electro technological installations, requires mathematical modeling for solving problems related to various physical phenomena, including electromagnetic (EM), thermal, mechanical, fluidic, and metallurgical fields. This article focuses on the solution of Maxwell's equations (MEs) and provides some basic information regarding the heat transfer and fluid equations, because these physical phenomena usually are strongly coupled to magnetic and electric fields. The solutions are usually obtained by using specific numerical methods such as finite-element method, finite difference method, boundary-element method or volume-integral method, and direct-solution method. The article also discusses the typical structure of commercial codes (preprocessor, solver, and postprocessor) to solve field problems mainly in finite-element method.

Fatigue crack growth rate testing and data analysis are performed to characterize the crack propagation resistance of material environment combinations in order to predict crack growth life under anticipated stress histories. This article presents analyses performed on the numerical output of crack growth rate tests, including the analysis framework for modeling fatigue crack growth rate data. It describes the numerical methods for calculating da/dN as a function of stress intensity factor. The article discusses the principles in fatigue crack growth damage analysis.

Ultrasound is an ideal modality for nondestructive evaluation (NDE) because it enables the interior of objects to be assessed without the safety and access issues associated with radiography. This article summarizes the history of array usage in NDE and its relationship to medical applications. It discusses the mathematics behind classical beamforming, full matrix capture, and total focusing methods of imaging. The article shows how ultrasonic array data can be simulated by direct numerical methods (most commonly using finite-element methods), analytical methods, or hybrid methods. It also considers various methods of comparing the performance of arrays and imaging algorithms. The article provides a comparison of various advanced and nonlinear imaging algorithm and looks at some practical industrial applications of arrays. It concludes with some future perspectives for arrays in NDE.

This article discusses the three different modeling approaches for grain structures formed during solidification of metallic alloys: direct modeling of dendritic structure, direct modeling of grain structure, and indirect modeling of grain structure. The main construction bases, the scale at which it applies, and the mathematical background are presented for each modeling approach. The article concludes with a table that presents a comparison of the main inputs/outputs, approximations, numerical methods, kinetics laws, and applications for the three approaches to modeling of dendritic grain solidification.

This article focuses on the directed-energy deposition (DED) additive manufacturing (AM) technique of biomedical alloys. First, it provides an overview of the DED process. This is followed by a section describing the design and development of the multiphysics computational modeling of the layer-by-layer fusion-based DED process. A brief overview of the primary governing equations, boundary conditions, and numerical methods prescribed for modeling laser-based metal AM is then presented. Next, the article discusses fundamental concepts related to laser surface melting and laser-assisted bioceramic coatings/composites on implant surfaces, with particular examples related to biomedical magnesium and titanium alloys. It then provides a review of the processes involved in DED of biomedical stainless steels, Co-Cr-Mo alloys, and biomedical titanium alloys. Further, the article covers novel applications of DED for titanium-base biomedical implants. It concludes with a section on the forecast of DED in biomedical applications.

Finite element analysis is a computer-based numerical method for solving engineering problems in bodies of user-defined geometry. This article introduces the important issues of finite elements (especially accuracy and efficiency) in a nonacademic manner. It describes the Rayleigh-Ritz procedure for solving structural problems based on the principle of virtual work. The article discusses continuum elements, such as hexahedra, pentahedra, tetrahedra, quadrilaterals, and triangles, commonly used in three- or two-dimensional domains. It considers structural elements such as beam element, plate element, shell element, and elbow element. The article presents three examples to illustrate the types of problems that can be addressed and the decisions that must be made when using finite element analysis.

Several methods are developed for the numerical solution of partial differential equations, namely, meshed-solution methods such as the finite-element method (FEM), finite-difference method, and boundary-element method; and numerical algorithms consisting of so-called meshed-solution methods. This article introduces the methods of so-called meshed solutions, with an emphasis on the FEM. It presents some basic differential equations that are used to model the responses of structures, components, processes, or systems with emphasis on continuum mechanics. The article provides an outline on the mathematical principles of solving differential equations. It also reviews linear structural problems to illustrate the concept of the FEMs.

This article discusses tools that are used for the systematic optimization of engineering designs. It focuses on the practical application of optimization technology in a computer-aided engineering environment. The article presents numerical optimization algorithms and provides some background on how these algorithms make decisions when searching for the optimal design. It also provides information on structural optimization, topology optimization, materials processing optimization, multidisciplinary optimization, and global optimization.

Fusion welding induces residual stresses and distortion, which may result in loss of dimensional control, costly rework, and production delays. In thermal analysis, conductive heat transfer is considered through the use of thermal transport, heat-input, and material models that provide values for the applied welding heat input. This article describes how the solid-phase transformations that occur during the thermal cycle produced by welding lead to irreversible plastic deformation known as transformation plasticity. Residual stress and welding distortion are also discussed.

Computational fluid dynamics (CFD) is reserved for computationally intensive three-dimensional simulations of thermal fluids systems where nonlinear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques for their solution. It introduces discretization techniques that are used by finite-difference, finite-volume, finite-element, spectral, and some particle methods. Associated concepts of numerical stability and accuracy are also reviewed. The article describes two approaches for grid generation with complex geometries: the use of unstructured grids and the use of special differencing methods on structured grids. The article describes the four-step procedures of the CFD process: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. It provides information on the applications of the engineering CFD. Issues and directions for the engineering CFD are also described.

Computational fluid dynamics (CFD) is a computationally intensive three-dimensional simulation of thermal fluids systems where non-linear momentum transport plays an important role. This article presents the governing equations of fluid dynamics and an introduction to the CFD techniques. It introduces some common techniques for discretizing the fluid-flow equations and methods for solving the discrete equations. These include finite-difference methods, finite-element methods, spectral methods, and computational particle methods. The article describes the approaches for grid generation with complex geometries. It discusses the four-step procedures used in the CFD process for engineering design: geometry acquisition, grid generation and problem specification, flow solution, and post-processing and synthesis. The article also provides information on the engineering applications of the CFD. It concludes with a discussion on issues and directions for engineering CFD.

Process optimization is the discipline of adjusting a process to optimize a specified set of parameters without violating engineering constraints. This article reviews data-driven optimization methods based on genetic algorithms and stochastic models and demonstrates their use in powder-bed fusion and directed energy deposition processes. In the latter case, closed-loop feedback is used to control melt pool temperature and cooling rate in order to achieve desired microstructure.

This article presents the modes of heat transfer and the stages of cooling during quenching. It provides an overview on the wetting process and then focuses on the evaluation of heat transfer during quenching. It also presents the challenges of thermal process evaluation based on an inverse heat conduction analysis. The article contains a compilation of best practice examples on heat transfer evaluation, which are intended to represent the practical aspects and applicability of the methods aiming the prediction of heat-transfer coefficients.

This article discusses the numerical simulation of the forming of aluminum alloy sheet metals. The macroscopic and microscopic aspects of the plastic behavior of aluminum alloys are reviewed. The article presents constitutive equations suitable for the description of aluminum alloy sheets. It explains testing procedures and analysis methods that are used to measure the relevant data needed to identify the material coefficients. The article describes the various formulations of finite element methods used in sheet metal forming process simulations. Stress-integration procedures for both continuum and crystal-plasticity mechanics are also discussed. The article also provides various examples that illustrate the simulation of aluminum sheet forming.

This article presents conservation equations for heat, species, mass, and momentum to predict transport phenomena during solidification processing. It presents transport equations and several examples of their applications to illustrate the physics present in alloy solidification. The examples demonstrate the utility of scaling analysis to explain the fundamental physics in a process and to demonstrate the limitations of simplifying assumptions. The article concludes with information on the solidification behavior of alloys as predicted by full numerical solutions of the transport equations.

This article summarizes many approaches that are used to simulate relaxation of bulk residual stresses in components. It presents analytical examples to highlight the complexity of residual stress and strain distributions observed in simple geometries, with ideal material behavior and trivial loading and boundary conditions. The article discusses approximate and advanced solution techniques that can be employed in practice for simulation of residual stress relief: finite-difference method and finite-element method. It also describes advanced techniques applicable to transient creep, advanced constitutive models, and complicated stress and temperature loading histories.

Friction stir welding (FSW) involves plastic deformation at high strain rates and elevated temperatures with resultant microstructural changes leading to joining. This article provides a link between deformation and FSW process parameters and summarizes the results of experimental temperature measurements during FSW of various metals. It considers the physical explanation of the heat input during FSW and the possible methods of their estimation. The article presents the experimental results of two analytical models, supplemented by experimental/numerical flow models on material flow during FSW. The types of defects, processing parameters affecting the generation of these defects, and results of theoretical models and simulations to understand the formation and control of defects during FSW are discussed. The article concludes with information on the microstructure and its distribution produced during FSW.

This article focuses on transport phenomena and modeling approaches that are specific to vapor-phase processes (VPP). It discusses the VPP for the synthesis of materials. The article reviews the basic notions of molecular collisions and gas flows, and presents transport equations. It describes the modeling of vapor-surface interactions and kinetics of hetereogeneous processes as well as the modeling and kinetics of homogenous reactions in chemical vapor deposition (CVD). The article provides information on the various stages of developing models for numerical simulation of the transport phenomena in continuous media and transition regime flows of VPP. It explains the methods used for molecular modeling in computational materials science. The article also presents examples that illustrate multiscale simulations of CVD or PVD processes and examples that focus on sputtering deposition and reactive or ion beam etching.