Computational Grid Research Articles

Modeling Object Motion on Arbitrary Unstructured Grids Using an Invariant Principle of Computational Domain Topology: Key Features

This paper uses a finite volume algorithm to address the numerical modeling of fluid flow around moving bodies. The Navier–Stokes equations, which describe the flow of viscous compressible gas, along with key boundary conditions and discretization schemes, are presented. As the motion of boundaries typically leads to changes in the control volumes, the basic discretization schemes need to be adapted. This paper provides a detailed discussion on the adaptation of the initial system to deforming boundaries while preserving communication topology. The method for calculating the boundary velocity is a crucial element of the numerical scheme. The paper proposes an approach to reconstruct the boundary velocity vector using deformation analysis and the condition of geometric conservation. This approach ensures correct simulation results for arbitrary unstructured computational grids. A comparison of two approaches to reconstructing the boundary velocity vector for characteristic aviation problems in the direct formulation is presented. It is shown that the proposed approach allows for more accurate modeling of object motion on arbitrary grids using the “invariant” principle of the computational domain topology.

Oscillation of an ultrasonically driven gas bubble in an asymmetric confined domain

This study numerically investigates the behaviour of an ultrasonically driven gas bubble between two parallel rigid circular walls with a cylindrical micro-indentation in one wall using the OpenFOAM software. The primary objective is to determine the conditions that facilitate the removal of particulate contamination from the indentation using the bubble jet. To accomplish this objective, various values of the indentation diameter D∗ were considered, ranging from 0 to 23. It was found that, when D∗<4.9, during the collapse phase, the bubble splits into two smaller sub-bubbles, within each of which a liquid jet emerges pointing towards the adjacent wall. Once the lower sub-bubble transforms into a toroidal shape, the high-speed liquid jet penetrates the indentation. This allows for the effective removal of particulate contamination present within the indentation specifically for cases where D∗<4. On the other hand, the lower sub-bubble completely vanishes when D∗≥4.9, rendering the removal of contamination impossible. It is important to note that for large values of D∗, there may exist situations in which numerical instability arises, resulting in the creation of artificial gas-filled regions within the liquid. We effectively resolve this issue through the proper treatment of the computational grid.

PHI-SMFE: spatial multi-scale feature extract neural network based on physical heterogeneous interaction for solving passive scalar advection in a 2-D unsteady flow

Fluid dynamic calculations play a crucial role in understanding marine biochemical dynamic processes, impacting the behavior, interactions, and distribution of biochemical components in aquatic environments. The numerical simulation of fluid dynamics is a challenging task, particularly in real-world scenarios where fluid motion is highly complex. Traditional numerical simulation methods enhance accuracy by increasing the resolution of the computational grid. However, this approach comes with a higher computational demand. Recent advancements have introduced an alternative by leveraging deep learning techniques for fluid dynamic simulations. These methods utilize discretized learned coefficients to achieve high-precision solutions on low-resolution grids, effectively reducing the computational burden while maintaining accuracy. Yet, existing fluid numerical simulation methods based on deep learning are limited by their single-scale analysis of spatially correlated physical fields, which fails to capture the diverse scale characteristics inherent in flow fields governed by complex laws in different physical space. Additionally, these models lack an effective approach to enhance correlation interactions among dynamic fields within the same system. To tackle these challenges, we propose the Spatial Multi-Scale Feature Extract Neural Network based on Physical Heterogeneous Interaction (PHI-SMFE). The PHI module is designed to extract heterogeneity and interaction information from diverse dynamic fields, while the SMFE module focuses on capturing multi-scale features in fluid dynamic fields. We utilize channel-biased convolution to implement a separation strategy, reducing the processing of redundant feature information. Furthermore, the traditional solution module based on the finite volume method is integrated into the network to facilitate the numerical solution of the discretized dynamic field in subsequent time steps. Comparative analysis with the current state-of-the-art model reveals that our proposed method offers a 41% increase in simulation accuracy and a 12.7% decrease in inference time during the iterative evolution of unsteady flow. These results underscore the superior performance of our model in terms of both simulation accuracy and computational speedup, establishing it as a state-of-the-art solution.

Assessment of stress-blended eddy simulation on prediction of flow characteristics in a Rushton impeller stirred tank

Stressed-blended eddy simulation (SBES), a novel hybrid RANS-LES approach, offers enormous potential to improve the prediction of the scale-resolving flow. However, few studies have been carried out on complex flow in stirred tanks. In this study, the SBES model was used to investigate the flow characteristics in a Rushton turbine stirred tank. The quantitative predictions of phase-averaged and phase-resolved flow field, as well as turbulence characteristics were conducted to assess the comprehensive performance of SBES. The results were also compared with those obtained from the SAS-SST model and LES model, as well as experimental data. It is indicated that the SBES model offers excellent agreement with experimental data in velocity and turbulence quantities, especially for the prediction of radial, tangential velocity and turbulent kinetic energy. Moreover, SBES model can successfully capture the features of trailing vortices and resolve more turbulence structure than the SAS-SST model with moderate computational grids.

The effect of segmentation depth in a helical fin tube bundle on the anisotropic turbulence state

The large eddy simulation approach was used to perform a numerical simulation of a flow around a helical segmented-fin tube bundle. This work focuses on the study of turbulence and the effect of segment depth on it. The simulation was conducted in an area away from the boundaries of the tube bundle, where the flow is fully-developed, and the use of periodic boundary conditions is possible. The computer-aided design of the helical segmented-fin tube geometry is incorporated into the computational grid from the immersed boundary technique. The Reynolds stress tensor was used to analyze the anisotropic state of turbulence. This flow is characterized by an anisotropic state generated by a flow with a preferential direction. A transfer of momentum in the inter-segment space and contiguous zones was observed. This intersegment flow generates a less anisotropic state of turbulence. This study aimed to understand a possible transformation of heat transfer with marginal geometrical changes and pressure drop increases.

The applicability of ALARO and AROME wind-fields in multi-scale waves forecasting in open sea and coastal areas of the southern Baltic Sea

The main objective of the study was to implement the wave model in two independent systems fed respectively by wind fields with a 4 km resolution in the Baltic-wide area and a 2 km resolution in the shallow coastal regions of the southern Baltic for operational work. The study included the selection the best parameterization, which was carried out using measured data and model data from the verified SWAN-COSMO system. The chosen best parameterization of the model, including the time step, iteration, wind scaling, dispersion coefficients and swell formula, among others, allowed the identification of the optimal system that guarantees the most reliable predictions. The most reliable forecasts reproducing real conditions, both for the model powered by wind fields with a resolution of 4 km and 2 km, were obtained for the configuration characterized by the parameters: 30-min time step, 3 iterations, a wind scaling factor of 32 using DEBIAS equal to 0.89, coefficients related to local dissipation and cumulative of 2.8 × 10–6 and 3.5 × 10–5, respectively, and Ardhiun's swell formula of 1.20. The values of the correlation coefficient with both the measured data and the results of the comparative model for significant wave height and wave period, respectively, were no lower than: 0.95 and 0.73 (Petrobaltic) and 0.96 and 0.90 (Pomeranian Bay). Root mean square error (RMSE) values were <0.23 m and <0.20 s (Petrobaltic) and <0.20 m and <0.74 s (Pomeranian Bay) for significant wave height and mean wave period, respectively. Analysis of the forecast results showed some limitations in using the mesoscale model in coastal areas, and the solution was to use the high-resolution model in this zone. It was shown that the stand-alone high-resolution model (domain: southern Baltic Sea) obtained similar results to the same model system but nested in the mesoscale model (domain: Baltic Sea). In addition, this model showed shorter simulation computation time and represents an independent, less vulnerable to discontinuity in forecast generation (lack of assimilation of boundary and initial conditions from a lower resolution model). A noticeable improvement in the quality of forecasts was shown by the AROME wind-field-powered model, which, due to its high resolution of the computational grid and wind data, maps well the wave dynamics in areas with limited wave exposure (the Vistula Lagoon, the Puck Lagoon) or complex coastline (the Hel Split) and seabed (the shallows of the Pomeranian Gulf and the Słupsk Shoal. The coupled data from the ALARO and AROME models, processed internally at IMWM-NRI, provide continuity and independence from global models and indicate applicability in generating wave forecasts by other Baltic countries.

Fast Meshless Solution With Lumped Friction for Laminar Fluid Transients

Abstract Fluid transients without friction in pipelines can be solved by a time-domain exact solution, using a simple recursive process without computational grid. However, the calculation time cost of this approach is very high because of the recursion algorithm. Its improved method, named as the fast meshless solution (FMS), was developed to speed up the computation by introducing time-line interpolation. However, when the friction is considered, the conventional distributed friction model cannot be employed directly for the FMS is meshless. To address this problem, the fluid friction is lumped at pipe ends, and both steady and unsteady laminar flow are investigated. Three kinds of lumped models are proposed here, and compared with a numerical case of the water hammer. The laminar fluid transients can be calculated quickly by the present method, with a little reduced accuracy. This method may be of interest in a quick assessment of the piping fluid transients.

Development of an Interpolated RANS-LES solver for wall-bounded turbulent fluid flows

Scale-resolving hybrid RANS-LES models are being increasingly used to numerically simulate wall-bounded turbulent flows since they are computationally efficient compared to LES (Large Eddy Simulation) while also being more accurate compared to RANS (Reynolds-Averaged Navier–Stokes) models. Existing hybrid RANS-LES models typically either suffer from modeled stress depletion or they can introduce a sharp jump in the mean Reynolds stress across the RANS-LES zone. We present a novel interpolated RANS-LES (IRL) solver implemented in OpenFOAM, in which the RANS equations (for eddy-viscosity) and LES equations (for filtered velocity) are evolved simultaneously on the same computational grid. Based on the distance from the no-slip wall, the flow domain is demarcated into a near-wall, free-stream, and a “hybrid” region, sandwiched between the near-wall and free-stream regions. Spalart Allmaras (S-A) model has been used to evolve the RANS eddy viscosity, while the Wall Adapting Local Eddy Viscosity (WALE) model is used for evolving the filtered LES velocity. Using a novel scheme based on solving a partial differential equation, the turbulent eddy-viscosity is interpolated between the RANS eddy viscosity in the near wall region and the effective eddy viscosity from the resolved LES fluctuations in the free-stream region. The mean subgrid stress in the LES momentum equation is then corrected in the near-wall and hybrid regions using the interpolated turbulent eddy-viscosity. IRL’s grid resolution requirements are the same as DES’s (Detached Eddy Simulation). Grid convergence and sensitivity studies have been carried out for two canonical flow geometries. For turbulent channel flow simulations, the IRL solver does not display the typical mean stress depletion observed in DES while also predicting resolved Reynolds stresses accurately in the free-stream region. For simulations of flow over backward facing step, the IRL solver can predict the friction factor and coefficient of pressure better than that DES, especially after the reattachment point.

Modelling and optimization of shallow underground thermal energy storage

Shallow geothermal reservoirs are excellent candidates for low-enthalpy energy storage, and can serve as heat batteries providing constant discharge of base heat, as well as rapid discharge of heat in periods of high demand. Recharging can be done by pumping down hot water, heated using excess heat from e.g. waste incinerators. In addition to having a very low carbon footprint, such systems also require limited surface infrastructure, and can easily be placed near or under the end-user, such as below residential buildings. The geological setting is typically complex, with horizons, faults, and intertwined patterns of natural fractures, and the nearwell region is often hydraulically fractured to enhance inter-well communication. Therefore, in order to fully utilize the potential of shallow geothermal heat storage, numerical simulations are imperative. In this work, we show how to practically model such systems, including generation of computational grids with a large number of wells and fractures, numerical discretizations with discrete fractures, and complex storage strategies with multiple wells working together under common group targets. We also discuss how adjoint-based methods can be used to tune model parameters (e.g. well injectivities, rock properties, and hydraulic fracture conductivities) so that the model fits observed data, and to find well controls (e.g. rates and temperatures) that optimize storage operations. The methodology is demonstrated using one artificial and two real underground thermal energy storage projects currently under development, and we highlight important challenges and our suggested solutions related to each of them. Thematic collection: This article is part of the Earth as a thermal battery: future directions in subsurface thermal energy storage systems collection available at: https://www.lyellcollection.org/topic/collections/thermal-energy

Large-Scale Cluster Parallel Strategy for Regularized Lattice Boltzmann Method with Sub-Grid Scale Model in Large Eddy Simulation

As an improved method of the lattice Boltzmann method (LBM), the regularized lattice Boltzmann method (RLBM) has been widely used to simulate fluid flow. For solving high Reynolds number problems, large eddy simulation (LES) and RLBM can be combined. The computation of fluid flow problems often requires a large number of computational grids and large-scale parallel clusters. Therefore, the high scalability parallel algorithm of RLBM with LES on a large-scale cluster has been proposed in this paper. The proposed parallel algorithm can solve complex flow problems with large-scale Cartesian grids and high Reynolds numbers. In order to achieve computational load balancing, the domain decomposition method (DDM) has been used in large-scale mesh generation. Three mesh generation strategies are adopted, namely 1D, 2D and 3D. Then, the buffer on the grid interface is introduced and the corresponding 1D, 2D and 3D parallel data exchange strategies are proposed. For the 3D lid-driven cavity flow and incompressible flow around a sphere under a high Reynolds number, the given parallel algorithm is analyzed in detail. Experimental results show that the proposed parallel algorithm has a high scalability and accuracy on hundreds of thousands of cores.

Grid-characteristic method using superimposed grids in the problem of seismic exploration of fractured geological media

Introduction.Seismic exploration in conditions of heterogeneity of the environment is an urgent topic for the oil and gas industry. Consequently, the development of numerical methods for solving the direct problem of seismic exploration remains relevant as a necessary link in the development and improvement of methods for solving the inverse problem. The Schonberg thin crack model has performed well in the numerical solution of problems requiring explicit consideration of geological inhomogeneities.Materials and Methods. In this paper, we consider a modification of the grid-characteristic method using superimposed grids. The presented approach makes it possible to conduct computational experiments, explicitly taking into account fractured inhomogeneities with arbitrary spatial orientation. For this, in addition to the basic regular computational grid, there is the concept of superimposed grids. Inhomogeneities, such as cracks, are described within the framework of the superimposed grid and, in turn, have no restrictions associated with the main grid. Thus, by performing an interpolation operation between the superimposed main grids, we can bypass the requirement of alignment of cracks and edges of the main grid.Results. The proposed approach made it possible to study the dependence of the anisotropy of the seismic response of a fractured cluster on the dispersion of the angles of inclination of the cracks.Discussion and Conclusions. A modification of the grid-characteristic method using superimposed grids is proposed to explicitly account for fractured inhomogeneities in a heterogeneous geological environment.

Grid-Characteristic Numerical Method on an Irregular Grid with Extending the Interpolation Stencil

A grid-characteristic numerical method for solving a multidimensional transport equation on an unstructured grid with an order higher than one is proposed; this method does not use auxiliary points on edges and faces. The avoidance of auxiliary points on edges and faces simplifies the topology of the computational grid during its motion, which is important for solving dynamic problems of mechanics of deformable solids. To increase the approximation order, an analog of the grid stencil extension implemented for an unstructured grid is used. Results of testing the proposed numerical scheme for continuously differentiable, continuous, discontinuous solutions are presented.

Оценка радиолокационного наукастинга полей осадков

The application of the Fraction Skill Score (FSS) to the radar nowcasting of precipitation fields is considered. The main feature of the method is that the quality is estimated not at the points (or cells) of the fields, but in their neighborhoods. Verification of field forecasts acquires a probabilistic character, due to which the well-known “double penalty” danger is eliminated when advancing from coarse computational grids to finer ones. Moreover, the method makes it possible to distinguish such range of scales within which the tested model generates forecasts that are acceptable or useful for both weather forecasters and third-party consumers of forecast products. The features and advantages of the FSS are demonstrated using the data of radar precipitation nowcasting in the warm and cold seasons of 2017–2018. An information archive of observation and forecast fields in the coverage areas of nine DMRL-C radars on the territory of the Central and Northwestern federal districts was used. Due to the large time spent to calculate the skill score, the possibility of obtaining summary estimates based on random samples was tested. Based on the output tabular and graphical verification products, meaningful general and partial conclusions are formulated that are stratified by seasons, radars, thresholds for exceeding the precipitation intensity, and the forecast lead time. Keywords: precipitation field nowcasting, radar observations, spatial forecast verification, neighborhood verification method, Fractions Skill Score (FSS)

ADER discontinuous Galerkin Material Point Method

AbstractThe first‐order accurate discontinuous Galerkin Material Point Method (DGMPM), initially introduced by Renaud et al. (J Comput Phys. 2018;369:80–102.), considers a solid body discretized by a collection of material points carrying the history of the matter, embedded in an arbitrary grid on which a nodal discontinuous Galerkin approximation is defined, and that serves to solve balance equations. This method has been shown to be promising, especially for solving hyperbolic problems in finite deforming solids (Renaud et al. Int J Numer Methods Eng. 2020;121(4):664–689. Renaud et al. Comput Methods Appl Mech Eng. 2020;365:112987.). The main goal of this research is to extend the first‐order DGMPM to arbitrary high‐order accurate approximations. This is performed by adapting the ADER (Arbitrary high order DErivative Riemann problem) approach (Busto et al. Front Phys. 2020;8:32.) to the particular spatial discretization of the DGMPM. First, the predictor step permits to design a particle‐to‐grid projection of arbitrary high order of accuracy, consistent with that of the nodal discontinuous Galerkin approximation defined on the arbitrary grid. This is performed using a moving least square approximation for the ADER predictor field. Second, since the degrees of freedom of the predictor field are now defined at material points, the computation of the constitutive response of the material is ensured to be always performed at these material points. This is of crucial importance for history‐dependent constitutive models because it avoids any diffusive transfer of internal variables on a new computational grid. Finally, a total Lagrangian formulation of equations is kept, which allows to precompute once and for all both the nodal discontinuous Galerkin approximation and that of the ADER predictor field, until the arbitrary grid is discarded if required. The method is illustrated on a few two‐dimensional numerical examples, on which comparisons are shown with the ADER‐DGFEM and Runge–Kutta‐DGFEM.

Study of the influence of the vessel stern shape on its hydrodynamic characteristics

Determining the main dimensions of the small vessels while designing is an important and difficult task due to the large number of mutually exclusive factors affecting the hydrodynamic characteristics of such vessels. The existing patterns for determining the length, width and draft of small vessels are quite general. This complicates their usage for the vessel of a specific design. In this case, it is necessary to check technical solutions, one of the ways that may be implied is the usage of computational fluid dynamics (CFD) methods. This paper presents the results of the numerical simulation of boat movement in the transient mode with Froude numbers up to 1.2. The process of preparation and numerical modeling of the aerodynamics of a composite wing in the NUMECA/FineMarineTM software package is described, the choice of the turbulence model and the parameters of the computational grid, including the resolution of the boundary layer, is justified. The study of the influence of three variants of the width and shape of the aft tip on the change in draft, trim angle, wetted surface and resistance of the boat is carried out. An increase in the width of the flat planing part of the aft tip has a favorable effect on the hydrodynamic characteristics of a small vessel, even when moving in transition mode at L/B from 3.5 to 3.99. At the same time, the use of the extension of the underwater part of the aft tip requires a more detailed study.

Emulation of seismic-phase traveltimes with machine learning

SUMMARY We present a machine learning (ML) method for emulating seismic-phase traveltimes that are computed using a global-scale 3-D earth model and physics-based ray tracing. Accurate traveltime predictions based on 3-D earth models are known to reduce the bias of event location estimates, increase our ability to assign phase labels to seismic detections and associate detections to events. However, practical use of 3-D models is challenged by slow computational speed and the unwieldiness of pre-computed lookup tables that are often large and have prescribed computational grids. In this work, we train a ML emulator using pre-computed traveltimes, resulting in a compact and computationally fast way to approximate traveltimes that are based on a 3-D earth model. Our model is trained using approximately 850 million P-wave traveltimes that are based on the global LLNL-G3D-JPS model, which was developed for more accurate event location. The training-set consists of traveltimes between 10 393 global seismic stations and randomly sampled event locations that provide a prescribed, distance-dependent geographic sample density for each station. Prediction accuracy is dependent on event-station distance and whether the station was included in the training set. For stations included in the training set the mean absolute deviation (MAD) of the difference between traveltimes computed using ray tracing through the 3-D model and the ML emulator for local, regional, and teleseismic distances are 0.090, 0.125 and 0.121 s, respectively. For tested station locations not included in the training set, MAD values for the three distance ranges increase to 0.173, 0.219 and 0.210 s, respectively. Empirical traveltime residuals for a global reference data are indistinguishable when ML emulation or the 3-D model is used to compute traveltimes. This result holds regardless of whether the recording station is used in ML training or not.

Insight into the dynamics of a Newtonian fluid through a rectangular domain with an emphasis on heat transfer

AbstractFluid flow coupled with temperature effects has attained prime importance due to its huge applications in different fields like casting and welding industries, geothermal extraction, and lubrication technologies. The present study is a novel numerical method for computations for fluid flow with temperature effects in a rectangular domain. A control volume method is employed as a numerical method for solving continuity, momentum, and energy equations. Owing to the difficulties associated with solving these governing equations, numerical computations are presented in the computational grid by using the control volume method. A modified algorithm is suggested for the current problem. The magnitude of the velocity, temperature, and pressure at different nodes in horizontal and vertical directions of the computational domain is investigated. Along the diagonal nodes, the pressure declines and then grows consistently. The temperature for mercury is higher than for water at a particular node.

Application of computational fluid dynamics for simulation of stirred bioreactors in Ansys Fluent

Stirred bioreactors are widely used in the pharmaceutical industry to produce various active substances for the treatment of cancer, heart and vascular diseases, viral and bacterial infections. Despite the widespread use of bioreactors with a stirrer, the optimization of mixing conditions remains an urgent task. In bioreactors of this type, continuous mixing of cells in a medium with a high rotation speed should be carried out. The manuscript considers an example of the use of computational fluid dynamics to study and model the process of cultivation Escherichia coli bacterial cells in a batch bioreactor (NLF, 30 l.). Computational fluid dynamics was used to analyze the hydrodynamic conditions in a bioreactor with a double Rushton turbine stirrer. To describe the movement of flows and evaluate turbulence in a batch bioreactor, the multiphase Euler model and the k-𝜀 turbulence model, respectively, were used, the built-in Ansys Fluent software package. A geometric model was built with the original dimensions of the bioreactor with an NLF 30 stirrer. Based on the geometric model, a computational grid was created for the working volume of the bioreactor and the optimal parameters for constructing the computational grid were selected. As a result of modeling the hydrodynamic regime, the distribution profiles of the turbulence kinetic energy over the volume of the bioreactor were obtained and the velocities of cell movement were found at different speeds of rotation of the stirrer. The obtained results show the possibility and applicability of the Ansys Fluent software package for calculating the hydrodynamic situation in a bioreactor with a stirrer at different stirring rates and at different cell volume fractions.

Assessing and improving strong-shock accuracy in the material point method

The Material Point Method (MPM) has appealing attributes for simulations involving large deformation of materials with history-dependent constitutive laws. It avoids the mesh tangling errors of Lagrangian finite element methods, as well as the advection errors typical of Eulerian or ALE methods. Recent developments in the MPM have led to a better understanding of the error and dissipation that arise in the particle-to-grid and grid-to-particle mapping, but significant error and high-frequency noise can still occur in simulations involving strong shock waves. This error appears to be associated with the kinematics on the background computational grid common to all MPM implementations. An investigation of forward- and reverse-ballistic impact simulations has revealed that sub grid-scale variations in the material state arise as the shock front enters a grid cell, and that this non-equilibrium state can persist unless the background grid has some means to relax the resultant particle-scale noise. Relaxation can occur when (i) the background grid shape functions have non-constant gradient, (ii) the shocked material has a sufficiently high velocity relative to the background grid, or (iii) the velocity field is enriched with additional degrees of freedom for treating weak discontinuities between particles.

Matlab Implementation using Holtrop and Mennen Method of Bare Hull Resistance Prediction for Surface Combatant Ship Coupled with CFD

Holtop’s &amp; Mennen’s method is one of the most widely used technique in resistance and powering prediction for tankers, general cargo ships, container ships and combatant surface ships. Holtrop’s Statistical Analysis method is utilized, as in comparison to the other options, more complete and closer to the actual results. The main purpose of this paper is to develop a Matlab application using Holtop’s &amp; Mennen’s method for studying and research the total resistance of DTMB 5415 combatant ship. The solid modelling is developed using Maxsurf. The computational fluid dynamic (CFD) technique is applied to analyze the hydrodynamic behaviour of hull form and predict the total resistance (Rt) to provide a description of the other prediction methods. The simulation process was executed using ANSYS software based on fluid flow (STAR-CCM+) solver. The variation of computational grid used in computation is SST (Shear Stress Transport) coarse and fine mesh size for hull speed up to 32 kn. RT resulted from CFD computation is validated with results from Holtrop that has been developed by Matlab implementation. The larger the grid meshing size, the better the validation of the results. The CFD technique demonstrated good agreement with Holtrop formulae in predicting the (RT) of DTMB 5415