A B-Spline Based Higher-Order Panel Method Applied to Marine Hydrodynamic Problems

2008 ◽  
Author(s):  
Chang-Sup Lee ◽  
Byoung-Kwon Ahn ◽  
Gun-Do Kim ◽  
Hyun Yup Lee ◽  
Do-Chun Hong
Keyword(s):  
Boundary Surface ◽  
Higher Order ◽  
Panel Method ◽  
Floating Bodies ◽  
B Spline ◽  
B Splines ◽  
Marine Propellers ◽  
Panel Methods ◽  
Infinite Extent ◽  
Blade Tip

A B-spline based higher order panel method (hereinafter, HiPan) is developed for the motion of bodies in ideal fluid, either of infinite extent or with free boundary surface. In this method, both the geometry and the potential are represented by B-splines, and it guarantees more accurate results than most potential based panel methods. In the present work, we apply the HiPan, which differs with the works at MIT in evaluating the induction integrals, to two major marine hydrodynamic problems: analysis of propulsive performance of the marine propellers and the motion of the floating bodies on the free surface. The present HiPan is shown superior to the constant panel method (hereinafter, CoPan) in predicting flow quantities in the area of the thin trailing edge and blade tip of the propeller. Numerical results are validated by comparison with experimental measurements.

A B-Spline Higher-Order Panel Method Applied to Two-Dimensional Lifting Problem

2003 ◽  
Vol 47 (04) ◽  
pp. 290-298
Author(s):  
Chang-Sup Lee ◽  
Justin E. Kerwin
Keyword(s):  
Present Method ◽  
Gaussian Quadrature ◽  
Solution Process ◽  
Higher Order ◽  
Panel Method ◽  
Pressure Jump ◽  
Two Dimensional ◽  
Kutta Condition ◽  
B Spline ◽  
Panel Methods

A higher-order panel method based on B-spline representation for both the geometry and the solution is developed for the solution of the flow around two-dimensional lifting bodies. The influence functions due to the normal dipole and the source are separated into the singular and nonsingular parts; then the former is integrated analytically, whereas the latter is integrated using Gaussian quadrature. Through a desingularization process, the accuracy of the present method can be increased without limit to any order by selecting a proper numerical quadrature. A null pressure jump Kutta condition at the trailing edge is found to be effective in stabilizing the solution process and in predicting the correct solution. Numerical experiments indicate that the present method is robust and predicts the pressure distribution around lifting foils with far fewer panels than existing low-order panel methods.

A B-spline based higher order panel method for analysis of steady flow around marine propellers

2007 ◽  
Vol 34 (14-15) ◽  
pp. 2045-2060 ◽  
Author(s):  
G.-D. Kim ◽  
C.-S. Lee ◽  
J.E. Kerwin
Keyword(s):  
Steady Flow ◽  
Higher Order ◽  
Panel Method ◽  
B Spline ◽  
Marine Propellers

Improved hydrodynamic analysis of marine propellers using a B-spline-based higher-order panel method

2015 ◽  
Vol 20 (4) ◽  
pp. 670-678 ◽  
Author(s):  
Gun-Do Kim ◽  
Byoung-Kwon Ahn ◽  
Ji-Hye Kim ◽  
Chang-Sup Lee
Keyword(s):  
Higher Order ◽  
Panel Method ◽  
Hydrodynamic Analysis ◽  
B Spline ◽  
Marine Propellers

A quartic trigonometric tension b-spline algorithm for nonlinear partial differential equation system

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Özlem Ersoy Hepson
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Burgers Equation ◽  
Higher Order ◽  
Spline Collocation ◽  
Partial Differential ◽  
Content Type ◽  
B Spline ◽  
B Splines ◽  
Coupled Burgers Equation

Purpose The purpose of this study is to construct quartic trigonometric tension (QTT) B-spline collocation algorithms for the numerical solutions of the Coupled Burgers’ equation. Design/methodology/approach The finite elements method (FEM) is a numerical method for obtaining an approximate solution of partial differential equations (PDEs). The development of high-speed computers enables to development FEM to solve PDEs on both complex domain and complicated boundary conditions. It also provides higher-order approximation which consists of a vector of coefficients multiplied by a set of basis functions. FEM with the B-splines is efficient due both to giving a smaller system of algebraic equations that has lower computational complexity and providing higher-order continuous approximation depending on using the B-splines of high degree. Findings The result of the test problems indicates the reliability of the method to get solutions to the CBE. QTT B-spline collocation approach has convergence order 3 in space and order 1 in time. So that nonpolynomial splines provide smooth solutions during the run of the program. Originality/value There are few numerical methods build-up using the trigonometric tension spline for solving differential equations. The tension B-spline collocation method is used for finding the solution of Coupled Burgers’ equation.

scholarly journals Improved Hydrodynamic Analysis of 3-D Hydrofoil and Marine Propeller Using the Potential Panel Method Based on B-Spline Scheme

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 196 ◽  
Author(s):  
Chen-Wei Chen ◽  
Ming Li
Keyword(s):  
Surface Pressure ◽  
Spline Interpolation ◽  
Pressure Coefficient ◽  
Panel Method ◽  
Hydrodynamic Performance ◽  
Surface Velocity ◽  
B Spline ◽  
Marine Propellers ◽  
Aspect Ratios ◽  
Thrust And Torque

In this paper, the hydrodynamic performance of lift-body marine propellers and hydrofoils is analyzed using a B-spline potential-based panel method. The potential panel method, based on a combination of two singularity elements, is proposed, and a B-spline curve interpolation method is integrated with the interpolation of the corner points and collocation points to ensure accuracy and continuity of the interpolation points. The B-spline interpolation is used for the distribution of the singularity elements on a complex surface to ensure continuity of the results for the intensity of the singular points and to reduce the possibility of abrupt changes in the surface velocity potential to a certain extent. A conventional cubic spline method is also implemented as a comparison of the proposed method. The surface pressure coefficient and lift the performance of 2-D and 3-D hydrofoils of sweepback and dihedral type with different aspect ratios are analyzed to verify the rationality and feasibility of the present method. The surface pressure distribution and coefficients of thrust and torque are calculated for different marine propellers and compared with the experimental data. A parametric study on the propeller wake model was carried out. The validated results show that it is practical to improve the accuracy of hydrodynamic performance prediction using the improved potential panel method proposed.

A Higher Order Time Domain Rankine Panel Method for Linear and Weakly Non-Linear Computation

2015 ◽  
Author(s):  
Felipe Ruggeri ◽  
Rafael A. Watai ◽  
Alexandre N. Simos
Keyword(s):  
Time Domain ◽  
Domain Boundary ◽  
Higher Order ◽  
Floating Body ◽  
Wave Runup ◽  
Floating Bodies ◽  
B Splines ◽  
Non Linear ◽  
Boundary Elements Method ◽  
Linear Effects

This paper presents a higher order time domain boundary elements method based on the Rankine sources for the computation of both linear and weakly non-linear effects for both fixed and free floating bodies. The geometry is described based on surfaces in a standard iges file, considering a NURBS (Non Uniform Rational Basis-Spline) description. The potential function, velocity, free-surface elevation and other quantities are defined using b-splines of arbitrary degree and the floating body interaction is solved using the potential acceleration approach on a Runge-Kutta scheme for time evolution. The integral equation is obtained and solved considering several possibilities for the collocation points, leading to an over-determined system. The integration over the panels is performed using a mixed desingularized-numerical method over Gaussian points. The results comparison are performed with WAMIT solution for a floating sphere concerning wave runup, body motions, velocity field, mean drift components in time domain.

scholarly journals Towards B-Spline Atomic Structure Calculations

Atoms ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 50
Author(s):  
Charlotte Froese Fischer
Keyword(s):  
Atomic Structure ◽  
Bound States ◽  
Virial Theorem ◽  
B Spline ◽  
B Splines ◽  
Self Consistent ◽  
History Of ◽  
Consistent Method ◽  
Atomic Structure Calculations ◽  
Structure Calculations

The paper reviews the history of B-spline methods for atomic structure calculations for bound states. It highlights various aspects of the variational method, particularly with regard to the orthogonality requirements, the iterative self-consistent method, the eigenvalue problem, and the related sphf, dbsr-hf, and spmchf programs. B-splines facilitate the mapping of solutions from one grid to another. The following paper describes a two-stage approach where the goal of the first stage is to determine parameters of the problem, such as the range and approximate values of the orbitals, after which the level of accuracy is raised. Once convergence has been achieved the Virial Theorem, which is evaluated as a check for accuracy. For exact solutions, the V/T ratio for a non-relativistic calculation is −2.

Generation and Modification of Non-Uniform B-Spline Surface Approximations to PDE Surfaces Using the Finite Element Method

1990 ◽  
Author(s):  
Joanna M. Brown ◽  
Malcolm I. G. Bloor ◽  
M. Susan Bloor ◽  
Michael J. Wilson
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Spline Approximation ◽  
The Finite Element Method ◽  
B Spline ◽  
B Splines ◽  
Spline Surface ◽  
Spline Surfaces ◽  
Spline Basis ◽  
Element Method

Abstract A PDE surface is generated by solving partial differential equations subject to boundary conditions. To obtain an approximation of the PDE surface in the form of a B-spline surface the finite element method, with the basis formed from B-spline basis functions, can be used to solve the equations. The procedure is simplest when uniform B-splines are used, but it is also feasible, and in some cases desirable, to use non-uniform B-splines. It will also be shown that it is possible, if required, to modify the non-uniform B-spline approximation in a variety of ways, using the properties of B-spline surfaces.

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