Semi Implicit Research Articles

Split-explicit external mode solver in the finite volume sea ice–ocean model FESOM2

Abstract. A novel split-explicit (SE) external mode solver for the Finite volumE Sea ice–Ocean Model (FESOM2) and its sub-versions is presented. It is compared with the semi-implicit (SI) solver currently used in FESOM2. The split-explicit solver for the external mode utilizes a dissipative asynchronous (forward–backward) time-stepping scheme that does not require additional filtering during the barotropic sub-cycling. Its implementation with arbitrary Lagrangian–Eulerian vertical coordinates like Z star (z*) and Z tilde (z̃) is explored. The comparisons are performed through multiple test cases involving idealized and realistic global simulations. The SE solver demonstrates lower phase errors and dissipation, while maintaining a simulated mean ocean state very similar to the SI solver. The SE solver is also shown to possess better run-time performance and parallel scalability across all workloads tested.

Numerical Analysis of Airflow in Trachea Affected by Thyroid Cancer Using Finite Volume Method

The study aims to analyze the airflow in the trachea due to thyroid cancer. Thyroid cancer is a cancer that attacks the thyroid gland. The thyroid gland is located in the neck below the Adam's apple. In general, thyroid cancer causes stenosis of the trachea due to cancer compression of the tracheal wall. This problem is solved using the finite volume method with SIMPLE (Semi Implicit Method for Pressure Linked Equation) discretization. This method is well suited for the discretization of irregularly shaped fluid flows. The software used is Matlab and Ansys Fluent. Matlab is used to compute numerical solutions and display graphs, while Fluent is used to visualize the air flow. The result of this study is that the greater the percentage of stenosis, the velocity of the airflow is faster and the pressure of the airflow is lower. The most critical condition for respiratory power loss is when the airflow velocity exceeds the normal limit, i.e. when the narrowing is more than 50%, the initial velocity is more than 0,1 m/s.

NUMERICAL ANALYSIS IN ARTERIAL STENOSIS AFFECTED BY ISCHEMIC HEART DISEASE USING FINITE VOLUME METHOD

Atherosclerosis is the narrowing of blood vessels caused by the buildup of cholesterol plaque on the walls of the arteries. Excessive buildup of cholesterol plaque disrupts the circulatory system, thereby affecting the speed and pressure of blood flow. In the long term, atherosclerosis can cause ischemic heart disease. This study aims to analyze the influence of stenosis, initial velocity, and diameter on the velocity and pressure of blood flow in narrowed arteries that cause ischemic heart disease. In this research, a Navier Stoke mathematical equation model was built which was solved using the finite volume method with SIMPLE discretization (Semi Implicit Method for Pressure Linked Equations). Finite volume methods are used to analyze unstructured objects such as blood flow. SIMPLE discretization is implemented simply in two and three dimensions with a system of equations containing fluid motion. Matlab and Fluent are software used for process simulations, Matlab for visualizing graphs of numerical calculation results, and Fluent for visualizing blood flow. Based on the simulation results, it can be concluded that the smaller the diameter, the greater the stenosis, and the greater the initial velocity, the greater the blood flow velocity. On the contrary, the diameter gets smaller, the stenosis gets bigger, and the initial velocity gets bigger so that the pressure on the blood flow gets smaller. Blood flow simulation has the potential to contain ischemic heart disease if the maximum speed produced is greater than the maximum normal blood speed, namely 0.45 m/s.

Thermal performance of Al2O3-TiO2/water hybrid nanofluids for cooling system using a helically coiled tube in a brushless direct current motor

Thermal performance of Al2O3-TiO2/water hybrid nanofluids for cooling system using a helically coiled tube in a brushless direct current motor has been investigated numerically. The numbers of helical coils number were varied by 4, 6, 8, and 10 in coils and represented by Helical numbers 362, 355, 352, and 350, respectively. To solve the velocity and pressure discretization, the SIMPLE (Semi Implicit Method for Pressure Linked Equations) method was applied whereas to solve the energy and momentum equations, second order upwind was used. The result revealed that Nusselt number of Al2O3-TiO2/water hybrid nanofluids is greater than water, with an increased Nusselt number of 3.7% and 10.42% for 1 vol.% and 2 vol.%, respectively. The added nanoparticles concentration of Al2O3-TiO2/water hybrid nanofluids could not reduce significantly the stator temperature. Al2O3-TiO2/water hybrid nanofluids can reduce the stator temperature by 0.92% and 1.82% for 1 vol.% and vol.2%, respectively compared to water. However, the increased Reynolds number can reduce the stator temperature for all the observed working fluids. Helical number can affect the Nusselt number due to the influence of the helical geometry on the fluid’s flow behavior, heat transfer properties, and turbulence levels. Nusselt number of Al2O3-TiO2/water hybrid nanofluids at 1 vol.% has a higher value than water in each variation with an average increase in Nusselt number of 4.12% for all helical numbers.

Stochastic Differential-Algebraic Equations in Power Systems–Semi Implicit Approach

Stochastic Differential-Algebraic Equations in Power Systems–Semi Implicit Approach

MHD flow of third-grade fluid through a vertical micro-channel filled with porous media using semi implicit finite difference method

This study examines the complex dynamics of an incompressible, electrically conducting third-grade fluid (TGF) flow through a vertical micro-channel that is filled with porous media. The research utilizes asymmetrical convective cooling, a transverse magnetic field, and exothermic reactions to introduce a comprehensive model. The viscosity of the fluid, which is determined by the Naham-type law, changes significantly with temperature. Additionally, the convective heat transfer rates, which govern the asymmetric convective cooling at the surfaces of the micro-channel, are modeled using Newton's law of cooling, and Modified Darcy law is used to address the porous medium effect. To solve the complex system of nonlinear partial differential equations, we employ computational solutions derived from reliable and efficient finite difference methods (FDM). The method is tested for different time-steps and mesh sizes and it is found that the algorithms reliably produce the same results. Our investigation includes an evaluation of both spatial and temporal convergence of the FDM scheme. The study present qualitative discussions of graphical results, that highlight the impact of various flow parameters integrated into the system. The velocity and temperature profiles increases for higher values of thermal Grashoff number Gr and Reynolds number Re while opposite effect is noticed for increasing values of Hartman number M.

Pressure gradient and an upstream cylinder on nanofluid flow around a heated cylinder: Heat transfer and entropy analysis

This study numerically investigates the nanofluid flow around a long heated cylinder of square cross-section (DSC) with height placed parallel to a cold wall at a fixed gap height The incident flow is Couette–Poiseuille (C–P) flow. Another cylinder of rectangular cross section (UREP) is placed on the upstream side in an inline arrangement with different gap spacings between the cylinders. The base fluid is chosen as the water and ethylene glycol–water mixture. Numerical experiments are made using staggered grid arrangement on non–uniform grid, finite volume methods, and Semi–Implicit Method for Pressure Linked Equations algorithm. Impact of pressure gradient at the inlet (due to C–P flow), position and shape (square/rectangular) of the UREP, nanoparticle concentration, and base fluid on the crowding of isotherms around edges of the DSC and hence to the heat transfer characteristics (Nusselt number and entropy generation rate density) is investigated. Bejan number is used to ratify that the irreversibility due to heat transfer is the major constituent of the total system irreversibility here. A reduction of heat transfer and entropy generation from the values of an isolated DSC is natural here due to the inline arrangement. An effort is made to improve the heat transfer by reducing the height of the UREP or/and by generating unsteadiness in the incoming flow to the DSC using a bluffer UREP or/and an increased pressure gradient. Finally, some scenarios are reported where the heat transfer decrement is less in comparison to that of the total system irreversibility.

High-Order Semi-implicit Schemes for Evolutionary Partial Differential Equations with Higher Order Derivatives

The aim of this work is to apply a semi-implicit (SI) strategy in an implicit-explicit (IMEX) Runge–Kutta (RK) setting introduced in Boscarino et al. (J Sci Comput 68:975–1001, 2016) to a sequence of 1D time-dependent partial differential equations (PDEs) with high order spatial derivatives. This strategy gives a great flexibility to treat these equations, and allows the construction of simple linearly implicit schemes without any Newton’s iteration. Furthermore, the SI IMEX-RK schemes so designed does not need any severe time step restriction that usually one has using explicit methods for the stability, i.e. Delta t = {mathcal {O}}(Delta t^k) for the kth (k ge 2) order PDEs. For the space discretization, this strategy is combined with finite difference schemes. We illustrate the effectiveness of the schemes with many applications to dissipative, dispersive and biharmonic-type equations. Numerical experiments show that the proposed schemes are stable and can achieve optimal orders of accuracy.

High order asymptotic preserving finite difference WENO schemes with constrained transport for MHD equations in all sonic Mach numbers

In this paper, a high-order semi-implicit (SI) asymptotic preserving (AP) and divergence-free finite difference weighted essentially nonoscillatory (WENO) scheme is proposed for magnetohydrodynamic (MHD) equations. We consider the sonic Mach number ε ranging from 0 to O(1). High-order accuracy in time is obtained by SI implicit-explicit Runge–Kutta (IMEX-RK) time discretization. High-order accuracy in space is achieved by finite difference WENO schemes with characteristic-wise reconstructions. A constrained transport method is applied to maintain a discrete divergence-free condition. We formally prove that the scheme is AP. Asymptotic accuracy (AA) in the incompressible MHD limit is obtained if the implicit part of the SI IMEX-RK scheme is stiffly accurate. Numerical experiments are provided to validate the AP, AA, and divergence-free properties of our proposed approach. Besides, the scheme can well capture discontinuities such as shocks in an essentially non-oscillatory fashion in the compressible regime, while it is also a good incompressible solver with uniform large-time step conditions in the low sonic Mach limit.

Multiscale solver for multi-component reaction–diffusion systems in heterogeneous media

Coupled nonlinear system of reaction–diffusion equations describing multi-component (species) interactions with heterogeneous coefficients is considered. Finite volume method based approximation for the space is used to construct semi-discrete form for the computation of numerical solutions. Two techniques for time approximations, namely, a fully implicit (FI) and a semi-implicit (SI) schemes are examined. The fully implicit scheme is constructed using Newton’s method and leads to the coupled system of equations on each nonlinear and time iterations which is computationally rather expensive. In order to minimize the latter hurdle, an efficient and fast multiscale solver is proposed for reaction–diffusion systems in heterogeneous media. To construct fast solver, we apply a semi-implicit scheme that leads to an uncoupled system for each individual component. Problems in heterogeneous domains require a very fine grid for accurate solutions of large systems of equations at each time step iteration. Here we present a multiscale model reduction technique to reduce the size of the discrete system. Multiscale solver is based on the uncoupled operator of the problem and constructed by the use of Generalized Multiscale Finite Element Method (GMsFEM). In GMsFEM we use a diffusion part of the operator and construct multiscale basis functions by solving spectral problems in each local domain associated with the coarse grid nodes. We collect multiscale basis functions to construct a projection/prolongation matrix and generate reduced order model on the coarse grid for fast solution. Moreover, the prolongation operator is used to reconstruct a fine-scale solution and accurate approximation of the reaction part of the problem which then leads to a very accurate and computationally effective multiscale solver. We provide numerical results for two species competition test problems in two-dimensional domain with heterogeneous inclusions. Our computed solutions predict strong competition between the two species and demonstrate that diffusion can dictate the dominance of one species over the other in heterogeneous environments. We investigate the influence of number of the multiscale basis functions to the method accuracy and ability to work with different values of the diffusion coefficients.

2D simulations of inductive RF heating in the drivers of the SPIDER device

This paper presents the basic physical and numerical principles of a fluid model of the negative ions source. The model gives self-consistent two-dimensional description of the source, including the neutral gas flow, plasma chemistry, RF coupling in the source driver and plasma transport through the magnetic filter. The different particle species (electrons, the three types of the positive ions: H+, H2+, H3+, negative ions H− and the neutral species: hydrogen atoms H and molecules H2) are described by separate continuity equations and the electron temperature is governed by the electron energy balance equation. The particle fluxes are found from momentum equations neglecting the inertia terms (drift-diffusion approximation). The electrostatic coupling between electrons and ions is described by the Poisson equation. The paper focuses on details of the RF model and on the initial code developments to simulate the currents in the source induced by the RF currents flowing in the feeding coils. In our approach, the RF electrical field is split in a plasma part plus another one in vacuum, E = Ep + EV, which simplifies the boundary conditions for Ep while EV is obtained from a theoretical formulation for the field generated by a current loop, which results in a fast and flexible numerical algorithm providing converged solution for the RF field after a few iterations, even for the cases with high conductivity of the plasma. The numerical method is based on finite volume approximation and 9-point discretization is used to account on anisotropy due to magnetic field. The semi implicit numerical solver allows for large time steps (>1000× explicit time step) producing steady-state solution in a reasonable time (few hours for a typical mesh). The RF model has been successfully coupled to the fluid equations of the source and self-consistent solutions are analyzed in order to see the influence of the driver parameters and RF model assumptions (e.g. stochastic conductivity, induced magnetic field) on the heating efficiency and the plasma dynamics. It has been found that without magnetic field the plasma dynamics in the SPIDER source is almost independent on the details of the RF coupling model.

Numerical analysis of air entrapment during water droplet impact on a substrate

As a liquid droplet impact on a substrate, it spreads flattens, and air may become trapped between the droplet and the substrate. This trapped air first evolves into an air film, which passes through many stages before eventually becoming an air bubble through retraction, contraction, toroid creation, pinching off, and so forth. The droplet cools while spreading across the substrate and finally freezes to create a splat. In most thermal spray coating applications, this phenomena is seen in the individual droplet solidification. The major purpose of this research is to develop an OpenFOAM solution that can model the effect of molten droplets on solid surfaces using free surface evolution. The PIMPLE algorithm, which is used in this solution, combines the PISO (Pressure Implicit with Splitting of Operators) and SIMPLE (Semi Implicit Method for Pressure-Linked Equations) approaches. In this approach, pressure–velocity equations are resolved, and the continuous surface flow model is used to simulate the surface tension force. Furthermore, the solution incorporates the dynamic contact angle. An enthalpy-based formulation that takes solidification into account is used to simulate the energy equation. The solver is validated with the aid of the available experimental results. Hydrodynamics can be used to properly simulate the various stages of air entrapment.

Fully developed forced convection H2O-CuO nanofluid flow through concentric pipes annular sector duct by using KKL model

Fully developed hydro-thermal H2 O- CuO nanofluid flow through concentric pipes annular sector duct is carried out. Koo–Kleinstreuer–Li ( KKL) model correlations are taken into account to discuss the forced convection flow under the effect of Brownian motion. For discretizing and numerical simulation of governing mathematical problem, finite volume based method, ( FVBM) and well known technique “semi implicit procedure for pressure linked equations, ( SIMPLE) revised” are utilized, whereas constant axial wall heat flux with uniform peripheral wall temperature and, constant and uniform wall temperature known as H1 and T thermally fully developed conditions respectively, are used to discuss the heat transfer rate for different contribution of “Copper Oxide ( CuO)” nanoparticles, n, in base fluid “pure water”. By adding the contribution of nanoparticles, the enhancement in fanning friction factor, fRe, and average Nusselt number, Nu, has been estimated upto 7.72% and 7.54% respectively, in H1 thermal case, whereas 7.71% and 7.16% respectively, in T thermal case.

Improvement of the Flow Pattern of a Forebay with a Side-Intake Pumping Station by Diversion Piers Based on Orthogonal Test Method

The flow analysis of the forebay of a lateral intake pumping station with asymmetrical operating pumps was carried out with a realizable k-ε turbulent model and SIMPLEC (Semi Implicit Method for Pressure Linked Equations Consistent) algorithm. The Pressure Inlet boundary condition was adopted and the pressure between the top surface and the bottom surface was linear with the height of the inlet section. The Mass Flow Outlet boundary condition was also adopted to ensure the accuracy and precision of the CFD (Computational Fluid Dynamics) simulation. The diversion pier was selected as the optimization strategy based on the flow parameters. The layout of the diversion piers was designed with four parameters which are the relative length, relative height, width, and straight-line distance of the piers’ tail. Each parameter had three values. Based on the orthogonal test, nine groups of the numerical simulation on different layouts of diversion piers were analyzed with the uniformity of axial flow velocity and weighted average angle of the flow velocity of the inlet cross-section of each pump, reducing the number of tests from 64 (43) groups to 9 groups, improving work efficiency. The results show that the diversion piers had a significant adjustment of uniformity of axial flow velocity and weighted average angle of flow velocity. After optimization of the forebay, the uniformity of axial flow velocity of intake of No.1 pump was 80.26% and the weighted average angle of flow velocity was 77.68°. The above values of the No.2 pump were 98.74% and 87.84°, respectively. The values of the No.4 pump were 93.41% and 77.28°. The results of numerical simulation, which was carried out to estimate the rectification effect under the operation combination of the No.1, No.3, and No.4 pumps, showed that the uniformity and the angle of the No.1 pump were 92.65% and 72.66°, respectively, the uniformity and the angle of No.3 pump were 94.54% and 85.14°, and the uniformity and the angle of the No.4 pump were 75.81% and 78.21°. This research proves that the orthogonal test method, in a reasonable and convenient way, can be applied in hydraulic optimization for a lateral intake pumping station.

The effect of Copper utilization on MSFR’s safety plug performance simulation by using MPS

Generation IV reactors are developed and expected to have a higher safety level than the previous reactors. One of the generation IV reactors is Molten Salt Fast Reactor (MSFR) with the freeze plug and drainage pipe as the integrated safety system. When an accident occurs, the fuel flows down, directly interacts and melts the freeze plug. Moreover, the fuel will be cooled at the safety tank. This research aims to simulate the freeze plug melting process by using Moving Particle Semi Implicit (MPS) method. MPS is a particle method based on Lagrangian mechanism developed by Koshizuka and Oka in 1996. Mainly, the freeze plug consisted of frozen salt and Hastelloy N. There were two kinds of freeze plug geometry used in the simulation, which were without and with copper. The copper thickness was varied between 1.5 - 3.0 mm with 0.5 mm intervals. The additional copper thickness was performed toward the inside of the freeze plug. The height and the radius of freeze plug were 30 mm. The thickness of Hastelloy N and the copper were 8.5 mm and 2.5 mm, respectively. S-curve temperature distribution was initially applied due to the heat transfer between molten salt and the freeze plug material. The results show the melting time of with and without copper cases were 125 s and 250 s, respectively. Moreover, the thicker copper led to the faster freeze plug melting process.

Simulation of Airflow Patterns and Aerodynamic Forces on a Chambered Airfoil and Symmetric Airfoil with Maximum Thickness Variation

Flow across the airfoil can cause drag and lift forces. The difference in pressure between the top and bottom surfaces of the airfoil creates a force that is perpendicular to the flow of fluid, and this force is called the lift force, and parallel to the flow is called the drag force. The author conducted research on simulating airflow patterns across the airfoil with maximum thickness variations. In this research, the simulation method is CFD (Computational Fluid Dynamic) using ANSYS Fluent software. The solution or solver method used in this simulation is the SIMPLE (Semi Implicit Method for Pressure Linked Equation) scheme. The flow pattern is shown by the streamline formed on the symmetric airfoil for α=0°, which will be symmetric, as well as the separation on the two sides, both the upper and lower sides. In contrast to the chambered airfoil, flow separation occurs only on the upper side. This indicates that there will be a pressure difference on the upper side and lower side so that the lift force can occur even though α=0°, because the lower side shows the pressure side. The greater the maximum thickness, the faster flow separation occurs. Then the higher the velocity value, the flow separation will be delayed due to an increase in the momentum of the working fluid flow, which overcomes the shear stress that occurs. At the angle of attack α=0°, the greater the maximum thickness of the chambered airfoil produces a greater lift force, while the symmetric airfoil does not produce lift.

A computational procedure and analysis for multi‐term time‐fractional Burgers‐type equation

This paper presents a new numerical algorithm dealing with multi‐term time‐fractional Burgers‐type equation involving the Caputo derivative. The proposed method consists of temporal discretization of formula and spatial discretization using the exponential B‐splines. The semi implicit approach is applied to discretize the nonlinear term . We adopt the Von–Neumann method to study stability. We also establish the convergence analysis. The proposed method is employed to solve a few numerical examples in order to test its efficiency and accuracy. Comparisons with the recent works confirm the efficiency and robustness of the proposed method.

FEM treatments for MHD radiative convective flow of MWCNTs C2H6O2 nanofluids between inclined hexagonal/hexagonal or hexagonal/cylinder

This paper aims to analyze the second law of the thermodynamic for the non-Newtonian power-law nanofluids flow between inclined polygonal/polygonal or polygonal/cylinder shapes. Multi-wall carbon nanotubes are incorporated in the ethylene glycol as a base fluid to formulate the worked suspension. Electromagnetic forces together with the thermal radiation are taken into account. Unusually, the magnetic field is assumed to be horizontal while the flow domain is inclined and a semi implicit treatment is presented for the magnetic terms. The solution methodology is depending on the Galerkin finite element method (FEM) and the Characteristic-Based Split (CBS) scheme. Various designs for the considered models are considered based on the areas and shapes of the inner polygonal/cylinder. The main outcomes revealed that area of the flow and power-law index N control in the convective and heat transfer process. Also, the fluid friction irreversibility takes its maximum values at high values of the power-law index. Furthermore, ratios of the increase in values of the entropy tools ( S T + , S F + , S tot + ) due to the variations of γ take their maximum at γ = 30 and low values of Ha .

A semi implicit compressible solver for two-phase flows of real fluids

The development of numerical solvers able to simulate compressible two-phase flows is still a great challenge in computational fluid dynamics. The interaction between acoustic waves and interfaces is of major concern for several engineering and biomedical applications, among which atomization in combustion chambers, cavitation problems, underwater explosions and bubble shock interactions. For instance, there are experimental evidences that acoustic waves can have an important effect on the atomization process, and this could have a great impact on combustion. However, usual approaches for DNS of primary atomization are based on incompressible solvers and therefore are not able to capture the propagation of acoustic waves and therefore cannot be used to simulate such phenomena. The numerical problem associated with the simulation of compressible two-phase flows is challenging, mostly because of the huge spatial variations of the speed of sound and the corresponding low Mach number in the liquid phase. In the present work, a numerical solver able to study subsonic compressible two-phase flows is presented. The solver is based on a complete formulation of the Navier-Stokes equations with real fluid equations of state, which are solved with a semi-implicit projection method. It is shown that the solver can handle a large range of compressible subsonic flows, both for a single phase or for two phases, as the flow induced by free convection, a bubble expansion in isothermal or isentropic conditions, and interaction between acoustic waves and liquid-gas interfaces. Eventually, attention will be given to the simulation of a water droplet in air, under the excitation of a stationary acoustic wave. It is also shown that the solver exhibits equivalent performances as an incompressible solver in configurations where compressible effects have no effects.

Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods

Numerical Treatment of Allen’s Equation Using Semi Implicit Finite Difference Methods