Abstract The solution of the volume fraction equations in multiphase flows has to satisfy geometric conservation, that is, the volume fraction fields at each control volume sum to 1. Enforcing this constraint on the volume fraction fields is critical for all multiphase flow applications especially for cases involving mass transfer. This article reviews some of the techniques used to enforce geometric

Abstract This work addresses an explicit methodology based on integral transforms for the inverse problem of reconstructing space and time dependent heat sources. The basic idea is to perform an integral transformation of the heat conduction equation and obtain an explicit expression for the integral transformed heat source in terms of the integral transformed temperatures. Once temperature measurements

Abstract The implicit discrete ordinates (SN ) discontinuous Galerkin (DG)/generalized minimal residual (GMRES) method has been implemented on shared-memory, multicore CPU/many-core GPU heterogeneous computation architecture via standard application programming interfaces (APIs) of open multiprocessing (OpenMP) and computer unified device architecture (CUDA). The compiler derivative based OpenMP parallelization

Abstract Numerical study of electro-osmotic flow (EOF) and theoretical exploration of relationship between EOF and electrical double layer (EDL) are carried out in the present work. Under the Poisson-Boltzmann and Debye-Hückel approximations, the analytic solution of electric potential, net charge, and flow pattern can be derived. The numerical results obtained by Poisson-Nernst-Planck (PNP) and Navier-Stokes

Abstract A new approach based on the Generalized Integral Transform Technique is advanced to deal with convective heat transfer in partially porous channels under local thermal nonequilibrium (LTNE) formulation. A semi-infinite partially porous parallel plates channel configuration is used to illustrate the semi-analytical solution methodology. The proposed eigenfunction expansion is based on a novel

Abstract A new concept of point mean beam length (PMBL) is introduced. For enclosures with simple geometry, this concept provides a fundamental self-consistent interpretation on the various different definition of the conventional mean beam length. The concept is further demonstrated to be effective in enhancing the computational efficiency for multidimensional radiative heat transfer in non-gray media

In this article, a finite volume formulation for solving the Navier-Stokes equations using unstructured hybrid grids and a staggered arrangement of variable pressure and velocity is presented. In this manner, a tight spatial pressure-velocity coupling is ensured without compromising geometrical flexibility. A second contribution of this work lays upon proposing a suitable interpolation function for

Flow pattern and heat transfer of flow boiling for different flow orientation, mini-channel width and height were presented in this work. The data were obtained by the numerical simulation with the coolant of R141b flow in a vertical mini-channel. Orientation includes upward and downward. A constant heat flux was loaded at the wall of the channel, of which the width ranges from 1 mm to 3 mm, and a

In the article, we solve the inverse problems to recover unknown space-time dependent functions of heat conductivity and heat source for a nonlinear convective-diffusive equation, without needing of initial temperature, final time temperature, and internal temperature data. After adopting a homogenization technique, a set of spatial boundary functions are derived, which satisfy the homogeneous boundary

In this article, the high-order upwinding combined compact difference scheme developed in a three-point grid stencil is applied to solve the incompressible Navier-Stokes (NS) and energy equations in three dimensions. The time integrator with symplectic property is employed to approximate the temporal derivative term in inviscid Euler equation so as to numerically retain the embedded Hamiltions and

In this study, the effect of oscillation amplitude on the pulsed impinging jets in different nozzle to surface distances and Reynolds numbers investigated. Generally, the heat transfer increases by increasing frequency and amplitude. For distances smaller and longer than the length of the jet potential core the threshold frequency is highly dependent on the amplitude. As the amplitude increases, the

Abstract In this study, the effect of oscillation amplitude on the pulsed impinging jets in different nozzle to surface distances and Reynolds numbers investigated. Generally, the heat transfer increases by increasing frequency and amplitude. For distances smaller and longer than the length of the jet potential core the threshold frequency is highly dependent on the amplitude. As the amplitude increases

Abstract This work aims to clarify and discuss, in a simultaneously accurate and simple way, some relevant issues on the stability and convergence of numerical solutions that are not usually presented in the literature and available for the students in this form. These include stability and physically realistic solutions of unsteady problems, and why the unconditionally stable Crank-Nicolson scheme

In this article, we developed a computationally efficient multilevel local radial basis function (RBF-FD) mesh-free algorithm. The algorithm provides a new strategy to get good order of accuracy with less computational time, which is most important in the present world. The main idea is the layer-by-layer calculation and then layer-by-layer correction from coarsest level to finest level node points

Natural convection in an inclined cavity filled with saturated porous media has been investigated. A time-dependent solution using a spectral weighted residual method is determined. Preparing the governing equations by the substitution of the stream functions, we obtained a system of nonlinear ordinary differential equations. Integrating in time using the Runge-Kutta method of variable order the final

Turbulent combustion models are substantially important in CFD simulation of combustion. Some simple models frequently cannot well simulate the finite-rate chemistry. Widely recognized models are good only for certain flame types and flame structures. More general is the PDF equation model, but its computation requirement is very large, in particular when using large-eddy simulation (LES). Alternatively

Abstract In this article, we developed a computationally efficient multilevel local radial basis function (RBF-FD) mesh-free algorithm. The algorithm provides a new strategy to get good order of accuracy with less computational time, which is most important in the present world. The main idea is the layer-by-layer calculation and then layer-by-layer correction from coarsest level to finest level node

Abstract Natural convection in an inclined cavity filled with saturated porous media has been investigated. A time-dependent solution using a spectral weighted residual method is determined. Preparing the governing equations by the substitution of the stream functions, we obtained a system of nonlinear ordinary differential equations. Integrating in time using the Runge-Kutta method of variable order

Abstract Turbulent combustion models are substantially important in CFD simulation of combustion. Some simple models frequently cannot well simulate the finite-rate chemistry. Widely recognized models are good only for certain flame types and flame structures. More general is the PDF equation model, but its computation requirement is very large, in particular when using large-eddy simulation (LES)

A Galerkin-based finite element recursion relation is used to solve the heat transport equation in two-dimensions. The finite element method (FEM) is a powerful technique that is commonly used for solving complex engineering problems. However, the implementation of the FEM in multi-dimensional problems can be computationally expensive. A finite element recursion algorithm based on bilinear triangular

Numerical simulations were carried out to study the heat transfer and friction characteristics for Stirling engine heater tubes with three-dimensional internal extended micro-rib. During the numerical simulations, phase angle in a cycle ranged from 0° to 360°. The results represent that the friction factor (f) increased with micro-rib length (L) and micro-rib height (H) for enhanced tube within the

Abstract A two-level variational multiscale meshless local Petrov-Galerkin (VMS-MLPG) method is presented for incompressible Navier-Stokes equations based on two local Gauss integrations which effectively replace a unit operator (first level) and an orthogonal project operator (second level). The present VMS-MLPG method allows arbitrary combinations of interpolation functions for the velocity and pressure

Abstract In this article, a new modified skew upwind differencing scheme (MSUDS) for convective flow is presented. This scheme is tested by pure advection test cases such as Step, Sine-square, Semi-ellipse, and Smith-Hutton test profiles. The benchmark lid-driven cavity flow problem is also solved with this MSUDS scheme. All the results are well plotted and validated. All the data regarding overshoots/undershoots

Abstract A Compressive volume-of-fluid (VOF) schemes exhibits numerical diffusion which inhibit them in obtaining a numerically sharp and wrinkle free description of fluid interface which is vital for understanding the complex interfacial dynamics. Therefore, the present study introduces a novel compressive VOF scheme capable of capturing sharp abrupt interfaces at stringent Courant conditions while

Abstract In this article, we propose a finite volume scheme preserving the discrete maximum principle (DMP) for steady heat conduction equations on distorted meshes. In contrary to these finite volume schemes preserving DMP, our new scheme uses the geometric average (instead of harmonic average) of two one-side numerical heat fluxes, especially it produces a more accurate flux approximation, which

Abstract A novel formulation for numerical solution of heat conduction problems using superposition of exact solutions (SES) to represent temperature on sub-elements of a region is described and demonstrated. A simple 1-D linear problem is used to describe the method and highlight potential benefits; however, extensions to higher geometric dimensions and linearization for temperature-dependent properties

Abstract This article presents a novel numerical method for steady-state thermal simulation. This method firstly solves the heat flux efficiently by applying the loop-tree basis functions. Then, the temperature is obtained by finding solutions of the gradient equation. The half boundary Rao-Wilton-Glisson (HBRWG) basis functions are employed for handling arbitrary boundary conditions. In addition,

Abstract The article deals with an implicit formulation of the pressure far field boundary condition, also known as the characteristic boundary condition, in a pressure-based coupled solver. This boundary condition applies to compressible flows over the entire Mach regime, and is derived by invoking the Riemann invariants to implicitly express the flow variables at inlets and outlets in terms of their

Abstract A continuum mixture model is proposed for phase change of binary alloy including the effect of thermal anisotropy. Thermal anisotropy is incorporated by an additional departure source in the conventional isotropic heat transfer-based energy equation. The governing equations for heat, mass, momentum, and species transport are solved using implicit finite volume method. The pressure and velocity

Abstract The SIMPLE algorithm is devised by interpolating the mass continuity and non-advective momentum equations, provoking apparent simplicity and clarity in the formulation. The SIMPLE variant entitled as the SIMPLE-AC scheme convokes an artificial compressibility (AC) parameter to augment the diagonal dominance of discretized pressure-correction equation. Both methods are characteristically pressure-based

Abstract The non-Newtonian fluids presenting viscoelastic flow behavior are found in many engineering applications. The development of a new numerical scheme for solution of this class of problems is the main goal of the present work. The proposed methodology adopts a second-order fully implicit finite difference approximation to discretize the convection and diffusion terms in the governing equations

This article deals with the development of an implicit and conservative method for conjugate heat transfer at solid-fluid interfaces. The technique is applicable for both conformal and non-conformal meshes. The method, which is implemented within a fully coupled in-house code, is symmetric in its treatment of the solid and fluid regions and is shown to be very robust for highly complex configurations

We present a novel hybrid scheme for the large eddy simulation (LES) of turbulent reacting flows. The scheme couples the discontinuous spectral element method (DSEM) solver for the unsteady compressible Navier-Stokes equations with a Monte Carlo particle filtered mass density function (FMDF) solver for the transport of reacting species. The method is capable of high-order simulations on unstructured

Unsteady laminar and turbulent pipe flows subjected to a constant temperature gradient in axial direction are investigated based on asymptotic considerations. The thermal boundary condition is that of a constant wall heat flux for a steady flow. The unsteadiness is induced by a sinusoidal pressure gradient with different amplitudes and frequencies. The asymptotic analysis is performed with the help

In the first part of this two-paper series, a new computational approach is presented for analyzing transient heat conduction problems in anisotropic nonhomogeneous media. The approach consists of a truly meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. In the present article, extensive numerical

In this article, a grad-div stabilized projection finite element method is proposed for the double-diffusive natural convection model. Moreover, for the presented method, the stability analysis, and error estimates are deduced. Finally, numerical tests are provided that demonstrate the efficiency of the method. It is found that the presented method can improve the accuracy of the solution compared

A new and effective computational approach is presented for analyzing transient heat conduction problems. The approach consists of a meshless Fragile Points Method (FPM) being utilized for spatial discretization, and a Local Variational Iteration (LVI) scheme for time discretization. Anisotropy and nonhomogeneity do not give rise to any difficulties in the present implementation. The meshless FPM is

Incompressible two-phase flow involving interface evolution was studied using a level set method. To maintain the level set function as a signed distance function from the zero level set and meanwhile preserve the mass conservation, a level set redistancing algorithm of level set methods was developed. Important to the above level set redistancing algorithm was a new idea that keeps the zero level

In this work, one three-dimensional periodic composite structure consisting of alumina frame and inscribed nickel spheres is proposed for designing the micron composite porous structure. The finite-difference time domain method is applied for predicting the radiation spectra of proposed composite structure and distribution of absorbed radiative power. The spectral characteristics of composite structure

In this article, a completely new numerical method called the Local Least-Squares Element Differential Method (LSEDM), is proposed for solving general engineering problems governed by second order partial differential equations. The method is a type of strong-form finite element method. In this method, a set of differential formulations of the isoparametric elements with respect to global coordinates

This work proposes a mechanical analog of the unsteady energy conservation equation for analysis of the stability of its numerical solution. The space discretized energy conservation equation is the analog of the linear momentum equation, from which no relevant information can be extracted concerning the stability of its numerical solution. The corresponding angular momentum equation can be obtained

One of the main factors affecting the heat transfer efficiency of solar collector is that the ordinary fluid in it is in the state of natural convection. Supercritical fluid is expected to improve the heat transfer efficiency of solar collectors due to its dramatic changes in thermal properties, so it is necessary to carry out the research of natural convection of supercritical fluid. Although researchers

In this article, a new interpolation method is developed for the Lagrangian statistics in the non-isothermal gas-solid flow. The Lagrangian statistics are inseparable from interpolation, especially the optimal interpolation. The new interpolation method in this article is developed based on the smooth Dirac delta function, which is also called delta function interpolation method (DFIM). The performance

The micro-channel heat dissipation system has minor specifications and good thermal conductivity per unit, which is the best choice for heat dissipation of micro-chips. By optimizing the cross section of microchannel, the heat exchange efficiency and temperature uniformity can be effectively improved. In this article, a double-layer triangular microchannel heat sink is proposed, which uniquely combines

(2020). Correction. Numerical Heat Transfer, Part B: Fundamentals: Vol. 77, No. 5, pp. 429-429.

Extensive computational investigations have been performed to obtain more detailed information about the peculiar phenomena of turbulent supercritical carbon dioxide (sCO2) flow as ideal heat transfer fluids in various thermal engineering applications. This paper reviews the simulation techniques used and discusses their advantages, shortcomings and applicability. Not only is a comprehensive inspection

To be a numerical method, the time-dependent convection boundary conditions are hard to be fulfilled exactly, which will deteriorate the accuracy of numerical solution. With this in mind, we develop novel algorithms to find the solutions for 1-D and 2-D heat equations, which can exactly satisfy the initial condition and convection boundary conditions. A new idea of space-time boundary shape functions

The field synergy principle has three criteria to qualitatively describe the essence of single-phase convective heat transfer enhancement. However, in practice these criteria are difficult to be applied to convective heat transfer analysis, because there are no corresponding indicators available to quantitatively describe them. Therefore, a unified formula for the field synergy principle was developed

This article presents a two-step iterative method that uses u – P formulation to study a Degasperis-Procesi (DP) equation, with which the DP equation is decomposed into the nonlinear advection equation and the Helmholtz equation. The first-order derivative terms in the advection equation are approximated by an Optimized Compact Reconstruction Weighted Essentially Non-Oscillatory (OCRWENO) scheme that

A new boundary-type meshfree collection method, namely the virtual boundary element-free Galerkin method (VBEFGM), is demonstrated for three-dimension (3-D) multi-domain steady-state heat conduction problems. The virtual source functions of the virtual nodes are constructed by the radial basis function interpolation. And the virtual and real boundaries are discreted into the virtual and real nodes

The flow and heat transfer characteristics of a droplet obliquely impact on a stationary liquid film is numerically studied by using a coupled level set and volume of fluid method (CLSVOF). The effects of impact angle, Weber number, and film thickness are analyzed. As compared with the normal impact, the flow features and surface heat flux distribution for oblique impact are asymmetric and where the

The effect of radial flow injection on the heat transfer characteristics of a Taylor–Couette–Poiseuille flow in an annulus is numerically investigated using the SST k-ω turbulence model. The ranges of the axial Reynolds number (ReA) and the rotational Reynolds number (ReΩ) are 6.58×104−1.37×105 and 7.19×104–1.8×105, respectively. For every combination of axial and rotational Reynolds number, flow is

The method of successive under-relaxation (SUR) is an effective way for numerically solving a nonlinear system of equations governing the fluid flow and heat transfer, resulting in stable convergence. So far, there is not any doable applied method to determine the best relaxation factor of SUR. In this article, the interrelation among the diffusion term, the convection term and the under-relaxation

This article devotes to the uncertain analysis of steady-state convection-diffusion heat transfer problems with interval input parameters in material properties, thermal source and boundary conditions. The optimization strategy is adopted to ensure a reliable bounds estimation when scales of interval width is larger, and a Galerkin system is derived to construct a Legendre Series Expansion (LSE) to

A numerical study of the forced convection of a two-dimensional laminar air flow through a rectangular pipe with a shoulder is presented. The profiles and contours of velocity and temperature were analyzed in detail. The effects of the location of this shoulder on the insulation and on the absorber, and its height on the variations of the temperature and the velocity at the exit of the collector were

A new space–time method, utilizing polynomials as the basis function, has been developed for solving time-dependent problems. Our proposed method does not have stability issues, nor does it require any parameters as were needed in the space–time radial basis function method, such as, the shape parameter, or those for the nodes distribution. In this article, various linear and nonlinear numerical examples

Thermal distortion characteristics of spiral groove gas face seals are investigated for cases of high temperature. The influence of ambient temperature and temperature difference on the thermal distortion and the sealing performance is analyzed with consideration of gas thermoviscosity effect. It is found that, the thermal distortion makes the opening force decrease slightly with the increasing ambient

This article presents an assessment of the scheduled relaxation Jacobi (SRJ) method for the solution of large-scale Poisson problems arising in the numerical simulation of large eddy turbulent flow in large complex geometry. The SRJ schemes are used both as standalone solvers and as preconditioners to Krylov subspace solvers. The Navier-Stokes equation is solved using structured Cartesian grids (both

The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. Part 1 of this two-part articles presents the process and characteristics of basic algorithms, including POD explicit and implicit time-marching methods. The accuracy and efficiency are verified by several numerical

The present work conducts a systematic and in-depth algorithm investigation for transient nonlinear heat conduction problems solved by using the proper orthogonal decomposition (POD) method. The computational results as presented in Part 1 have revealed some signatures of the basic algorithms, in which poor efficiency is its main shortcoming. In this article, as Part 2, several advanced algorithms