Pressure Boundary Research Articles

Applications of finite difference‐based physics‐informed neural networks to steady incompressible isothermal and thermal flows

AbstractPhysics‐informed neural networks (PINNs) have aroused an upsurge in scientific machine/deep learning community, especially in research areas involving solving partial differential equations. In this work, based on the multilayer perceptron neural network and finite difference (FD) method, we apply the finite difference‐based PINNs (FD‐PINNs) to simulate the steady incompressible flows. The spatial derivatives in nonlinear governing equations are discretized by the central FD scheme, and the physical boundary conditions can be exactly satisfied in a similar way to conventional fluid flow solvers. Compared to original PINNs using automatic differentiation (AD) to discretize the governing equations, FD‐PINNs hold three‐fold potential advantages in decoupling the predictive accuracy of derivatives from the network's approximating accuracy, fulfilling the physical boundary conditions, and saving computational costs when large‐size networks or meshes are used. We first attempt to make relatively fair comparisons between AD‐PINNs, FD‐PINNs and conventional flow solvers using a benchmark flow problem—steady incompressible laminar isothermal lid‐driven cavity flow across a wide range of Reynolds numbers (Re). Our results indicate that FD‐PINNs are superior to AD‐PINNs in both predictive precision, computational efficiency and training convergence. Moreover, FD‐PINNs exhibit higher accuracy than flow solvers when insufficient mesh points are used to solve high‐Re cavity flow. Even at Re = 10,000, with only 10 internal samples, FD‐PINNs can still precisely recover the flow details on a uniform mesh of size 51 × 51. Besides, the time consumption of FD‐PINNs grows much slower than that of conventional flow solvers. We also investigate the robustness of FD‐PINNs w.r.t. the noise level of samples and the effects of pressure boundary condition imposed on solid cavity walls. Furthermore, FD‐PINNs are extensively applied to predict the incompressible thermal flows: natural convective flows in a square cavity and in a concentric annulus, where the effects of governing equations on the predictive accuracy are discovered and discussed for the first time.

Uncovering the effects of local pressure and cooling rates on porosity formation in AA2060 Al-Li alloy

The third generation of Al-Li alloys (e.g. AA2060) have been widely used in aerospace engineering. The formation of porosity during casting is a major obstacle for improving its mechanical properties due to the 10 times the equilibrium hydrogen concentration in the liquid than the traditional aluminum alloys. In this study, the effects of two fundamental parameters are investigated: cooling rate and pressure on the formation of porosity. The centrifugal casting process was used to apply external pressure during solidification and quantify the 3D porosity morphology as a function of the external parameters using X-ray computed tomography (X-CT). Subsequently, a Cellular Automata (CA) model was used to predict porosity as a function of pressure and thermal boundary conditions. It was found that the externally applied compressive pressure contributes to porosity closure within certain limits. In addition, the cooling rate not only refines the grain size but also minimizes porosity defects by increasing their number density, and the experimental results validated the predictions by the CA model. By increasing the solidification pressure and cooling rate, a high-performance AA2060 Al-Li alloy with a tensile strength of 490 MPa and an elongation of 6.1% was obtained.

Effect of bainitic or martensitic microstructure of a pressure vessel steel on grain boundary segregation induced by step cooling simulating thermal aging

During operating lifetime of a nuclear power plant, the pressure boundary components, usually in 16MND5 (SA508 Cl. 3) steel, are subjected to thermal aging that may induce phosphorus intergranular segregation. This is known to decrease brittle fracture stress and induce intergranular fracture, which causes reversible temper embrittlement. Large components such as the reactor pressure vessel presents microstructure heterogeneity due to forging and welding. Tempered martensite can locally be found in the nominally bainitic steel. The question of microstructure susceptibility to reversible temper embrittlement has been raised in literature suggesting that tempered martensite has higher sensibility to phosphorus intergranular segregation than tempered bainite. In this paper, a comparative study of intergranular segregation in tempered bainitic and martensitic 16MND5 steel after thermal aging is conducted using energy dispersive X-ray spectroscopy on transmission electron microscope. Focus ion beam is used to precisely prepare lamellae at prior austenite grain boundaries on step cooled bainitic and martensitic samples. Different types of grain boundaries are identified using precession assisted crystal orientation mapping and then the local chemical composition is analyzed. Phosphorus, nickel, manganese and molybdenum were observed at all types of grain boundaries in both microstructures. The segregation levels are higher in prior austenitic grain boundaries than in other types of boundaries for both microstructures. Taking into account the segregation amount in different types of boundaries, the phosphorus bulk depletion is shown negligible. The results show similar segregation levels in the two studied microstructures, indicating that the susceptibility to thermally induced grain boundary segregation between the tempered bainite and tempered martensite is the same.

Multi-scale finite element simulation of the thermoforming of a woven fabric glass fiber/polyetherimide thermoplastic composite

Understanding the thermoforming process for thermoplastic composites is of great importance to ensure the quality of the composite product but is difficult because of the complex material constitutive models and thermo-mechanical coupling in the thermoforming process. In this study, a woven fabric thermoplastic composite consisting of glass fiber and polyetherimide resin was thermoformed under one-sided cooling conditions. After the effective material properties are homogenized with newly developed, two-step asymptotic homogenization methods, and the temperature and pressure boundary conditions are measured experimentally, a 3D composite laminate sandwiched by interfacial layers and metal molds was finite element simulated in the macroscale. The simulated warpage, which was caused by the in-plane residual stresses, was consistent with the experimental results when reasonable tool–part interactions were considered. Subsequently, the temperature, displacement, strain, and stress were comprehensively discussed in terms of their spatial distribution, temporal evolution, and correlations with the others.

Simulation of multiphase behavior in supercritical CO2–heavy oil–water sludge extraction systems using Cubic-Plus-Association Equation of State

A new methodology was proposed for predicting the multiphase behavior of a supercritical CO2–heavy oil–water–solvent system during supercritical CO2 extraction. The cubic-plus-association equation of state (CPA EoS) was used to model the hydrogen bond association between asphaltene and water and to develop a nine-step characterization method for asphaltene-containing oil. Results showed that the proposed method could represent phase behavior for three equilibrium phases: the vapor phase and high-density and low-density liquid phases. The absolute average relative deviation between the predicted and experimental phase boundary pressures was 3.6–11.8%, smaller than those (7.0–20.8%) calculated using Soave–Redlich–Kwong EoS with Huron–Vidal mixing rules. Moreover, case studies on appropriate extraction conditions showed that the extraction pressure increased with increasing molecular weight and critical pressure of each pseudocomponent. Increasing extraction pressure for H2O-containing systems was beneficial for improving extraction efficiency.

Simulation based analysis to study the effect of compression ring crown height in ring liner assembly on the performance of four stroke petrol engine

Among different piston rings of an Internal Combustion Engine (IC), the top compression ring-liner assembly shared a momentous amount of the total frictional losses, particularly at the Top Dead Center (TDC) and Bottom Dead Center (BDC) where boundary lubrication subsists. In the present study, the lubrication mechanism in piston ring cylinder liner conjunction for top compression ring using one dimensional Reynolds equation assuming axisymmetric contact was studied. The hydrodynamic and mixed lubrication regimes were taken during the study. Gumbel boundary conditions were used for Reynolds equation solution. For boundary pressure calculation, first, combustion chamber pressure variation was determined, then, interring pressure was calculated assuming orifice volume method by solving mass flow rate through crevice volumes using Runge-Kutta 4th order method. The Reynolds equation was solved using finite difference method. Whole solution process was repeated for different engine speed and crown height of top compression ring to study the effect of them in wear and power loss. First, the solution was found for 3000, 5000 and 7500 RPM keeping constant crown height of 10 µm. Average power loss was found to be increased with the increasing engine speed. There was increased in oil film thickness around mid-stroke with the increased engine speed, but there was no significant change in film thickness with the engine speed at the TDC and BDC positions. Then, the solution was again repeated for different RPM varying the crown height. The compression ring with lower crown height showed the better wear performance by increasing the minimum film thickness in critical zones of engine cycle for all RPM. The crown height of 5,7 and 9 µm gave the minimum power loss (77.89, 163.47 and 297.33 W) for 3000, 5000 and 7500 rpm. Moreover, the power loss in the range of 5-9 µm had no significant differences.

Performance Comparison of Helium and sCO2 as Coolants for Modular Finger-Type Divertors

Several studies at the Georgia Institute of Technology have evaluated the thermal and fluids performance of the helium-cooled modular divertor with multiple jets (HEMJ) over the past decade. This finger-type divertor was studied both experimentally at nearly prototypical conditions and numerically at fully prototypical operating conditions using experimentally validated simulations. Recently, supercritical carbon dioxide (sCO2) has been studied as the primary coolant in power cycles and other applications in various systems, in part because CO2 achieves the high densities typical of supercritical fluids at relatively low temperatures and pressures, with a critical point of (7.38 MPa, 31°C). This density makes it possible to realize very compact and efficient sCO2 power cycles. The feasibility of sCO2 as a coolant for plasma-facing components, specifically the divertor, was therefore evaluated as part of the Fusion Energy System Studies design study activities. This work compares the thermal-fluid performance of helium and sCO2 in the HEMJ divertor geometry using numerical simulations at prototypical conditions: inlet temperatures Ti = 600°C to 700°C, pressures p ≈ 10 MPa, and steady-state incident heat fluxes on the tile q″ < 17 MW/m2. The performance is quantified here as the maximum heat flux that can be accommodated by the plasma-facing tile, the pumping power fraction, defined as the ratio of the coolant pumping power to the incident thermal power, and the operating stress limits based on ASME pressure vessel criteria. As expected, helium requires lower mass flow rates and pumping power fractions within imposed maximum temperature limits for the HEMJ pressure boundary. However, it also appears that neither helium nor sCO2 can remove 10 MW/m2 of incident heat flux while meeting ASME pressure vessel criteria. Finally, the numerical modeling reveals that sCO2 may remove slightly higher incident heat fluxes than helium due to the imposed stress limits due to the sCO2 coolant resulting in smaller local temperature gradients, albeit at a considerably higher pumping power fraction.

ASU model with multiple adjustment types for oxygen scheduling concerning pipe pressure safety in steel enterprises

Steel production requires enough oxygen, which is produced by cryogenic air separation (ASU) with a large load, high power, and slow adjustment. Facing complex oxygen demands, effective ASU scheduling can reduce energy waste and has great potential for low-carbon development. Current ASU scheduling models have only a sole load-adjustment type. To address the limitation, a novel scheduling framework model is researched for ASUs with various load-adjustment types, and is applied to an oxygen system scheduling mode1 for steel enterprises. In addition, current multi-period oxygen scheduling models have an issue that time discretization leads to oxygen pipe pressure deviation between model calculation and practical operation and impacts on system safety. Therefore, a novel method to compensate for pressure boundaries is studied to precisely handle the deviation. Some contrast tests concerning various load-adjustment types of ASU are conducted with simulative and real data. The simulative tests indicate that the framework can both unify multiple adjustment types (MAT) and flexibly migrate among various ASUs. In the real scenario, the oxygen scheduling model with the MAT-ASU avoids oxygen emission and reduces comprehensive cost (including electricity consumption and oxygen release loss) of the manual scheduling by 24%. The MAT enhances the response ability to complicated demands, thereby performing better to optimize the comprehensive cost. Though smaller pipe volume or larger discrete period size increases the pressure deviation, the compensation method perfectly ensures safe system operation.

Empirical investigation of interzonal air leakage and airborne sound transmission correlation in multi-unit residential buildings

In the context of suite compartmentalization in multi-unit residential buildings, knowing the airtightness of individual pressure boundaries (e.g. floor, corridor wall, suite wall, etc.) is imperative for the diagnosis and remediation of issues such as regulating ventilation air delivery and managing pollutant transfer. However, conventional quantification methods, such as the pressure neutralization method, are cumbersome to complete. The feasibility of an acoustic testing approach, which leverages the relationship between increased air leakage rate and decreased airborne sound transmission loss was examined. Limited studies have explored this relationship in building enclosure elements, and no attempts were made to assess the correlation in interior partitions. In-situ measurements were conducted across twelve suite partition walls from three multi-unit residential buildings to obtain experimental correlations between the two parameters. The area-normalized air leakage rate at 50 Pa (q50) varied among specimens of the same composition, demonstrating the importance of air-sealing details for the overall partition airtightness. The variation in q50 was best reflected by the area-normalized sound transmission loss at 630 Hz; a non-linear model and the inclusion of air pressure differential information also improved the models’ accuracy. While the root-mean-square error of 0.56 L/s/m2 in q50 prediction suggests this acoustic approach needs further refinement to verify compliance with increasingly stringent compartmentalization targets, the current study demonstrates the application and potential benefits of the acoustic approach in a real-world context. Further data could improve the model so that it could be suitable for screening partitions with similar construction and in pre- and post-retrofit comparisons.

Calculation method of friction coefficient on flat plate in supercritical water laminar boundary layer flow

In supercritical water (SCW) gasification reactor, understanding the interaction of SCW with wall surfaces and the boundary layer situation is significant to gasification efficiency improvement. This paper wishes to find a convenient way to calculate the friction coefficient on flat plate in SCW laminar flow with a pseudo-critical incoming state. The velocity profiles characteristics in the SCW boundary layer would be studied using direct numerical simulation (DNS) method, and they would be applied to variable separation of friction coefficient expression. Then, a semi-analytical formula for plate friction applied to the SCW fluid field would be derived, and it would be found to be the extended form of that derived from the Blasius's theory. In this formula, the effects of the unique properties variation around critical points had been isolated as dimensionless parameter Gμ*, dependent on pressure and temperature boundary conditions. The method of obtaining Gμ* by DNS will be given, and two details in the processes will be explained. Finally, the dependence between Gμ* and boundary conditions would be derived by numerical experiments. By the semi-analytical formula and diagram of Gμ*(Tw)|in, the friction coefficient on one side of the plate in SCW laminar flow could be quickly calculated. The applicable inflow states are five pseudo-critical points of 23–27 MPa, the wall temperature is 645–673 K, and the Reynolds number range is above 1×105. The accuracy of this method has been proved by comparing the results obtained by it with DNS results.

Numerical and boundary condition effects on the prediction of detonation engine behavior using detailed numerical simulations

High-fidelity numerical simulations of an experimental rotating detonation engine with discrete fuel/air injection were conducted. A series of configurations with different feed-plenum pressures but with constant equivalence ratio were studied. Detailed chemical kinetics for the hydrogen/air system is used. A resolution study for the full rotating detonation engine (RDE) system simulation is also conducted. Two kinds of boundary conditions, a total pressure boundary and a constant mass flow rate boundary, are used to assess the effects of the inlet boundary. As mass flow rate is increased, the total pressure boundary causes more error in the axial pressure distribution while the constant mass flow rate gives a better solution for all cases ran. The simulations confirm experimental findings, and reproduce qualitative as well as some of the quantitative trends. These results demonstrate that a) fuel-air mixing is highly non-uniform within the detonation chamber, leading to variations in local equivalence ratio, b) the fuel and oxidizer injectors experience significant backflow as the detonation wave passes over, but recover at different rates which further augments the inefficiencies in mixing, and c) parasitic combustion in the mixing region makes the detonation wave weak by extending the reaction zone across the wave.

An unconditionally stable artificial compression method for the time‐dependent groundwater‐surface water flows

AbstractIn this article, we propose a second order, unconditionally stable artificial compression method for the fully evolutionary Stokes/Darcy and Navier‐Stokes/Darcy equations that model the coupling surface and groundwater flows. It uncouples the surface from the groundwater flow by the Crank‐Nicolson Leapfrog scheme for the discretization in time, and through the artificial compression method without artificial pressure boundary conditions to decouple the velocity and pressure of the incompressible flow. Finally, we have verified the stability and second‐order convergence of the algorithm from theoretical analysis and numerical experiments.

A Three-Dimensional Analytical Solution of Stress Field in Casing-Cement-Stratum System Considering Initial Stress State

Accurate stress field calculation of the casing-cement-stratum system is crucial for evaluating wellbore integrity. Previous models treated in-situ stress as boundary pressure loads, leading to unrealistic infinite displacements at infinity. This study presents a three-dimensional (3D) analytical solution for the stress field within the casing-cement-stratum system in inclined wells, considering in-situ stress and hydrostatic stress in cement as the initial stress state and taking into account stress components related to the axial direction. Assuming a plane strain condition and superimposing the in-plane plane strain problem, elastic uni-axial stress problem and anti-plane shear problem, a 3D analytical solution is obtained. Comparisons with previous models indicate that the existing model overestimates the absolute values of stress components and failure potential of casing and cement in both 2D and 3D scenarios. The presence of initial stress in cement greatly increases the absolute value of the compressive stress state but decreases the failure potential in cement, which has not been well studied. Additionally, a low Young’s modulus and high initial stress state of the cement benefits the cement’s integrity since the maximum Mises stress significantly decreases. The new 3D analytical solution can provide a benchmark for 3D numerical simulation and quick assessment for wellbore integrity.

Investigation of the Processes Occurring During the Operation of the Torque Converter Hub in the Belarusian Autoworks Gearbox during CAE Modeling

The main objective of the study is to identify and eliminate the causes of breakdowns in the torque converter hubs of mining dump trucks Belarusian Autoworks. The relevance of the work carried out: during the operation of dump trucks based on Belarusian Autoworks vehicles, in open pit conditions, according to enterprises operating such equipment, in the period from 2019 to 2021, 75% of the failures and breakdowns of equipment occurred due to the fact that the hub of the torque converter impeller is intensively loaded a part, which during its operation is affected not only by mechanical loads, but also by temperature and others leading to the failure of the specified unit in 85% of cases. For example, hydrodynamic forces that arise during the period of immersion of gear teeth in an oil bath, and so on. Therefore, it is proposed to conduct a comprehensive study of the processes occurring with the wheel hub and identify the main loaded places. Taking into account the analysis carried out, it is possible to produce a batch of wheel hubs with updated parameters and conduct their full-scale tests. The novelty of the work carried out lies in the analysis of the operating conditions of the hub, which revealed a high boundary pressure that occurs at the point of transition from the air to the oil bath. The object of research is the study of the processes that occur during the operation of the torque converter hub, which affect the structure and occur in the hub itself. Research objectives: - learn the ways and methods of conducting CAE analysis; - analyze the design parameters of the installation that occur in the torque converter bushing. Research methods: When performing the dissertation work, methods of physical and mathematical modeling and system analysis of information, laboratory, bench and operational tests using computer and high-precision measuring equipment were used

A Numerical Study on the Influence of Cerebrospinal Fluid Pressure on Brain Folding

AbstractOver the past decades, the buckling instability of layered materials has been the subject of analytical, experimental, and numerical research. These systems have traditionally been considered with stress-free surfaces, and the influence of surface pressure is understudied. In this study, we developed a finite element model of a bilayer experiencing compression, and found that it behaves differently under surface pressure. We investigated the onset of buckling, the initial wavelength, and the post-buckling behavior of a bilayer system under two modes of compression (externally applied and internally generated by growth). Across a wide range of stiffness ratios, 1 &amp;lt; μf/μs &amp;lt; 100, we observed decreased stability in the presence of surface pressure, especially in the low-stiffness-contrast regime, μf/μs &amp;lt; 10. Our results suggest the importance of pressure boundary conditions for the stability analysis of bilayered systems, especially in soft and living matter physics, such as folding of the cerebral cortex under cerebrospinal fluid pressure, where pressure may affect morphogenesis and buckling patterns.

Applying surface tension as pressure boundary condition in free surface flow analysis by moving particle simulation method

A model that introduces surface tension as a pressure boundary condition, named the surface tension as pressure (STP) model, was developed for free surface flow analyses by the moving particle simulation (MPS) method. The STP model assigns to surface particles the liquid pressure of Laplace’s formula. The model is an alternative to previous models that apply surface tension as volume force such as the continuum surface force model. Problems that appeared when using the volume force models, such as the dependencies of calculation results on particle resolution and pressure gradient accuracy, were solved by using the STP model. Calculations predicted the theoretical values of the internal pressure of a 3D spherical droplet and the oscillation period of a 2D elliptic droplet over a wide range of surface tension coefficients and droplet sizes with errors less than 10%. Since the STP model is easy to implement, does not increase computation cost from previous models, and does not require surface reconstruction or additional marker particles, the model is suitable for practical and large-scale free surface flow problems that involve violent deformation of the liquid surface such as liquid atomization.

Existence of a solution to the non-steady magnetohydrodynamics-Boussinesq system with mixed boundary conditions

In this paper we are concerned with the non-steady magnetohydrodynamics (MHD)-Boussinesq system with mixed boundary conditions. The boundary conditions for fluid may include the stick, pressure, vorticity and stress conditions together, and in the case of static pressure may include the friction type of boundary conditions more. For the magnetic field, a non-homogeneous mixed boundary conditions are given. The conditions for temperature may include Dirichlet, Neumann and Robin conditions together. For the problem involving the static pressure and stress boundary conditions for fluid it is proved that if the data of problem are small enough, material parameters are independent of temperature, then under compatibility conditions in the initial time there exists a strong solution and the solution with small norm is unique. Much effort is paid to overcome a difficulty in dealing the advection term, Lorentz force in the momentum equation of fluid and a nonlinear term in the magnetic equation under the static pressure boundary conditions on a portion of boundary where there is flux of fluid and non-homogeneous magnetic boundary conditions. For the problem involving the total pressure and total stress boundary conditions for fluid, the existence of a solution is proved without smallness of the data of problem.

An Improvement in Boundary Treatment of Solid Boundary Using ISPH Approach

Incompressible Smoothed Particle Hydrodynamic (ISPH), one of the particle methods, is frequently employed to address a variety of challenging physical issues, such as those involving free surface flow. For measuring the precise and reliable pressure close to the boundary, the study of boundary treatment has lately been an active research field in the mesh-free or particle approach. If the solid barrier's appropriate pressure boundary condition is not met, fluid particles may penetrate it. This study proposes a straightforward boundary treatment that can satisfy the non-homogenous Neumann boundary condition on the solid boundary and the Dirichlet condition on the water surface. The main idea behind our suggested approach is that by solving a modified pressure Poisson equation, these boundary conditions are automatically satisfied. This technique can be improved such that it can be applied to any shape having a concave-convex boundary in addition to basic solid boundaries. The suggested method was tested using the hydrostatic case, followed by a numerical analysis validated using a 3D dam break flow with an opening gate and a Stanford rabbit demonstration. The outcome of the numerical modelling simulation was then contrasted with the findings of the theoretical and experimental studies. The obtained findings support the suggested technique by providing a good tendency and similarity output that enhances the boundary treatment on solid boundaries.

Co-Simulation Modeling and Multi-Objective Optimization of Dynamic Characteristics of Flow Balancing Valve

The poor dynamic characteristics of the flow balance valve used in a ship’s HVAC system are the main reasons for the hydraulic imbalance and high energy consumption of the system. A new adjustable dynamic flow balance valve structure is designed, which is composed of a self-operated pressure regulator and an electric V-shaped ball valve in series. When the V-shaped ball valve is fully opened at the 20 t/h flow level, the dynamic characteristics of the flow balance valve cannot meet the requirements. A new co-simulation method that combines MATLAB/Simulink and the UDF dynamic grid is proposed to study the dynamic characteristics of a flow balance valve with a 20 t/h flow rate under different pressure drop step signal interference. When the calculation of each micro-element time converges, the valve core motion parameters, the pressure boundary conditions, the valve core axial medium force, and the valve outlet flow are interactively transmitted in the two simulation environments. The discrepancy between the co-simulation and test results is less than 5%, which verifies the accuracy of the co-simulation model. Aiming at the most severe dynamic characteristic working condition where the pressure drop is stepped from 30 to 300 kPa, the influence of different structural parameters on the dynamic characteristics of the balance valve is analyzed. A new surrogate model combining RSM and RBF with the co-simulation method improves the optimization efficiency and fitting accuracy. To improve the convergence of the traditional NSGA-II algorithm, key structural parameters are optimized by combining the NSGA-II algorithm and SDR. The test results show that the dynamic characteristics of the optimized valve are improved, the discrepancy between the stabilized flow rate and 20 t/h does not exceed 4.5%, and the flow is relatively constant. Therefore, the proposed co-simulation and optimization method can be applied to the dynamic characteristic prediction of self-operated valves, such as dynamic flow balance valves, to provide guidance for developing high-precision self-operated valves.

A Cartesian grid-based two-dimensional plus time method for simulating ship bow waves

Numerical modeling of ship bow waves is still hard work, partly due to their multiscale features. Direct three-dimensional (3D) computational fluid dynamics simulation could be an appropriate choice to investigate the problem. However, limited by computational resources, small scale phenomena such as spraying and wave breaking that could be observed during the ship wave generation process are usually simplified or not fully distinguished in a 3D simulation. In order to accurately capture the small scales flow field information with the available computational resource, a new Cartesian grid-based two-dimensional plus time (2D+t) method is developed in this paper, which is suitable for 3D slender ships. With this method, a 3D steady ship wave-making problem is transformed into a 2D unsteady wave-making problem of a deformable body. The boundary velocity of the deformable body is obtained with a novel interpolation algorithm, which is then enforced on the background Cartesian grid by a newly proposed immersed boundary method. The pressure boundary condition on the surface of the deformable body is explicitly considered in the solution of the pressure Poisson equation. Moreover, an extra open boundary condition is applied to the upper boundary of the computational domain to achieve a better conservation. The proposed model is validated with selected cases, showing that the model is capable of simulating both non-wave-breaking and wave-breaking problems.