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A one-sided direct forcing immersed boundary method using moving least squares [article]

Rahul Bale, Amneet Pal Singh Bhalla, Boyce E. Griffith, Makoto Tsubokura
<span title="2021-04-15">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
This paper presents a one-sided immersed boundary (IB) method using kernel functions constructed via a moving least squares (MLS) method.  ...  Prior IB/MLS methods have used isotropic kernel functions that coupled fluid variables on both sides of the boundary to the interfacial degrees of freedom.  ...  A. Kernel functions Here we write the one-dimensional form of some of the kernels used in this work. In multiple dimensions, a tensor product of the one-dimensional kernels is formed.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.07738v1">arXiv:2104.07738v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/bopatlh6n5ehpiggjlf4yx7g2y">fatcat:bopatlh6n5ehpiggjlf4yx7g2y</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210420015826/https://arxiv.org/pdf/2104.07738v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/71/6c/716c15cf5d1f32a4e6ff6ab172573d1668196892.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2104.07738v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

A sharp interface direct-forcing immersed boundary method using the moving least square approximation

Mehdi BADRI GHOMIZAD, Hosnieh KOR, Koji FUKAGATA
<span title="">2021</span> <i title="Japan Society of Mechanical Engineers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/m3pzcr3ynfcx5garcrfockcefm" style="color: black;">Journal of Fluid Science and Technology</a> </i> &nbsp;
Based on the Moving Least Square (MLS) approximation, we propose a sharp interface direct-forcing immersed boundary method for incompressible fluid flows with fixed and moving boundaries.  ...  To alleviate the inherent spurious numerical oscillation that occurs in the calculated forces on moving boundary embedded objects, we use a two step predictor-corrector method in which the direct forcing  ...  on the whole solid domain while the data is transferred between the Eulerian and Lagrangian nodes by using a direct moving least square approximation.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1299/jfst.2021jfst0013">doi:10.1299/jfst.2021jfst0013</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/hyovfb2zyzbr3ee2s6xxwlgkd4">fatcat:hyovfb2zyzbr3ee2s6xxwlgkd4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20210717171755/https://www.jstage.jst.go.jp/article/jfst/16/2/16_2021jfst0013/_pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/99/40/99400ab2bfd42cc6132eae9338c4afa75ef23227.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1299/jfst.2021jfst0013"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

On immersed boundary kernel functions: a constrained quadratic minimization perspective [article]

Amneet Pal Singh Bhalla
<span title="2021-11-23">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In the IB literature, the regularized delta functions, also referred to IB kernel functions, are either derived analytically from a set of postulates or computed numerically using the moving least squares  ...  In the immersed boundary (IB) approach to fluid-structure interaction modeling, the coupling between the fluid and structure variables is mediated using a regularized version of Dirac delta function.  ...  Moving least squares method The standard formulation The standard formulation of the moving least squares method considers the following approximation problem.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2111.11025v2">arXiv:2111.11025v2</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/q5ptutwmabh7tmm7jdqdt6d27i">fatcat:q5ptutwmabh7tmm7jdqdt6d27i</a> </span>
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An implementation of the direct-forcing immersed boundary method using GPU power

Bulent Tutkun, Firat Oguz Edis
<span title="2016-10-13">2016</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/tmsw2hzmzbhmhpcigrajn3c6b4" style="color: black;">Engineering Applications of Computational Fluid Mechanics</a> </i> &nbsp;
A graphics processing unit (GPU) is utilized to apply the direct-forcing immersed boundary method.  ...  The second test case is the simulated flow around a circular cylinder. This case was selected to better understand the effects of sharp corners on the force coefficients.  ...  A direct-forcing approach is utilized for the immersed boundary method.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/19942060.2016.1236749">doi:10.1080/19942060.2016.1236749</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/nwpxghmotfejxiqgfn5nmhuah4">fatcat:nwpxghmotfejxiqgfn5nmhuah4</a> </span>
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A structured adaptive mesh refinement strategy with a sharp interface direct-forcing immersed boundary method for moving boundary problems

Mehdi BADRI GHOMIZAD, Hosnieh KOR, Koji FUKAGATA
<span title="">2021</span> <i title="Japan Society of Mechanical Engineers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/m3pzcr3ynfcx5garcrfockcefm" style="color: black;">Journal of Fluid Science and Technology</a> </i> &nbsp;
We develop a versatile and accurate structured adaptive mesh refinement (S-AMR) strategy with a moving least square sharp-direct forcing immersed boundary method (IBM) for incompressible fluid-structure  ...  An IBM using a moving least square approach is utilized to impose boundary conditions.  ...  to the fixed boundary problems (Popinet, 2003) , the present method is based on a shared-memory parallel solver, which allows us to efficiently utilize the moving least square sharp interface immersed  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1299/jfst.2021jfst0014">doi:10.1299/jfst.2021jfst0014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ms2z5ezohvhlxjsekqp7ijuu4a">fatcat:ms2z5ezohvhlxjsekqp7ijuu4a</a> </span>
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A Stress Mapping Immersed Boundary Method for Viscous Flows

Karim M. Ali, Mohamed Madbouli, Hany M. Hamouda, Amr Guaily
<span title="2021-10-06">2021</span> <i title="Akademia Baru Publishing"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/65zk4tqmlraktarpvmwute4kie" style="color: black;">Journal of Advanced Research in Fluid Mechanics and Thermal Sciences</a> </i> &nbsp;
The method uses flow field mapping on the immersed boundary and performs a contour integration to calculate immersed boundary forces.  ...  The governing equations of the fluid mechanics are solved using a Galerkin-Least squares finite element formulation.  ...  In this work, the pressure-stabilized incompressible Navier-Stokes equations [25, 26] were solved using a Galerkin-Least Squares (GLS) finite element method following [27] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37934/arfmts.87.3.120">doi:10.37934/arfmts.87.3.120</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/gycnajujcfaevljmszobwkk55a">fatcat:gycnajujcfaevljmszobwkk55a</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211014011210/https://www.akademiabaru.com/submit/index.php/arfmts/article/download/3641/3155" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/d2/3b/d23b0dce9c3b30bd51b3150488a7dd334796647a.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.37934/arfmts.87.3.120"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An explicit and non-iterative moving-least-squares immersed-boundary method with low boundary velocity error [article]

Wenyuan Chen and Shufan Zou and Qingdong Cai and Yantao Yang
<span title="2021-10-19">2021</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
In this work, based on the moving-least-squares immersed boundary method, we proposed a new technique to improve the calculation of the volume force representing the body boundary.  ...  A spatially uniform coefficient is then introduced to correct the force and fixed by the least-square method over all boundary markers.  ...  The baseline moving-least-squares immersed-boundary method For the volume force f b in Eq. ( 1 ), we adopt the MLS-IBM as the baseline method.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.13612v1">arXiv:2110.13612v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/vdb76syhsfcnnhr43jhg2esdo4">fatcat:vdb76syhsfcnnhr43jhg2esdo4</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20211103011427/https://arxiv.org/pdf/2110.13612v1.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/65/a9/65a99b57e357a767cbd74b13beb3165999ea45bf.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/2110.13612v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Radial basis function (RBF)-based interpolation and spreading for the immersed boundary method

Francisco Toja-Silva, Julien Favier, Alfredo Pinelli
<span title="">2014</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wp3g5bo4ojczdinvl7cavuwkq4" style="color: black;">Computers &amp; Fluids</a> </i> &nbsp;
Immersed boundary methods are efficient tools of growing interest as they allow to use generic CFD codes to deal with complex, moving and deformable geometries, for a reasonable computational cost compared  ...  In this work, we propose a new immersed boundary method based on a radial basis functions framework for the spreading-interpolation procedure.  ...  , we use a classical least square method to compute the regularized force f i : W T W f = W T b. (25) Before proceeding further, a word of caution is due.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.compfluid.2014.09.026">doi:10.1016/j.compfluid.2014.09.026</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/mwxrnvtolbhppj3ox5xaiid5ey">fatcat:mwxrnvtolbhppj3ox5xaiid5ey</a> </span>
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A unified interpolation stencil for ghost-cell immersed boundary method for flow around complex geometries

Hosnieh KOR, Mehdi BADRI GHOMIZAD, Koji FUKAGATA
<span title="">2017</span> <i title="Japan Society of Mechanical Engineers"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/m3pzcr3ynfcx5garcrfockcefm" style="color: black;">Journal of Fluid Science and Technology</a> </i> &nbsp;
We propose a unified interpolation stencil that is used for a ghost-cell immersed boundary method to satisfy wall boundary conditions in Cartesian-based numerical simulation of fluid flow with complex  ...  Performance of the proposed method is studied by solving two-dimensional incompressible flows around a circular cylinder, a square cylinder, and a square cylinder inclined with respect to the main flow  ...  The ghost points are the nodes nearest to the physical boundary that have at least one neighbor on the fluid side. To do so, a proper description of the physical boundary would be invaluable.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1299/jfst.2017jfst0011">doi:10.1299/jfst.2017jfst0011</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/suwnwzg7jnbazoqwakmiecylcu">fatcat:suwnwzg7jnbazoqwakmiecylcu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20181101133548/https://www.jstage.jst.go.jp/article/jfst/12/1/12_2017jfst0011/_pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/51/44/514487d67e85a3dbf4f1a3899a68cb1972f1bbbc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1299/jfst.2017jfst0011"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> Publisher / doi.org </button> </a>

An accurate moving boundary formulation in cut-cell methods

Lennart Schneiders, Daniel Hartmann, Matthias Meinke, Wolfgang Schröder
<span title="">2013</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
., it generates unphysical oscillations in the hydrodynamic forces exerted on the moving boundary.  ...  We focus on eliminating unphysical oscillations occurring in Cartesian grid methods extended to moving-boundary problems.  ...  [28] considered this case to demonstrate that unphysical force oscillations can appear in the immersed boundary method with moving boundaries and direct forcing.  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2012.09.038">doi:10.1016/j.jcp.2012.09.038</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/a6yfyuwlxjgw3melndi62hwmbu">fatcat:a6yfyuwlxjgw3melndi62hwmbu</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170812234548/http://www.aia.rwth-aachen.de/vlueb/staff/homes/84/publications/Schneiders13_preprint.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/77/9f/779f38f9bf2c6d1a772b57169c7ffe6b935517c6.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2012.09.038"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a>

A sharp-interface immersed boundary method with improved mass conservation and reduced spurious pressure oscillations

Jung Hee Seo, Rajat Mittal
<span title="">2011</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/f7kkigxhzjakref5b42jt4uoya" style="color: black;">Journal of Computational Physics</a> </i> &nbsp;
A method for reducing the spurious pressure oscillations observed when simulating moving boundary flow problems with sharp-interface immersed boundary methods (IBMs) is proposed.  ...  By first identifying the primary cause of these oscillations to be the violation of the geometric conservation law near the immersed boundary, we adopt a cut-cell based approach to strictly enforce geometric  ...  Other immersed boundary based approaches also show spurious oscillations in the forces exerted on the moving body [9] .  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2011.06.003">doi:10.1016/j.jcp.2011.06.003</a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pubmed/21857745">pmid:21857745</a> <a target="_blank" rel="external noopener" href="https://pubmed.ncbi.nlm.nih.gov/PMC3156558/">pmcid:PMC3156558</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/fcm6c4hkgjgtra5aszfm5yijym">fatcat:fcm6c4hkgjgtra5aszfm5yijym</a> </span>
<a target="_blank" rel="noopener" href="https://web.archive.org/web/20170830065451/https://engineering.jhu.edu/fsag/wp-content/uploads/sites/23/2014/06/JCP_Seo_Mittal_2011_2.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> Web Archive [PDF] <div class="menu fulltext-thumbnail"> <img src="https://blobs.fatcat.wiki/thumbnail/pdf/f2/53/f253ec6067ef9e86e8e411aa161368e9c865cccc.180px.jpg" alt="fulltext thumbnail" loading="lazy"> </div> </button> </a> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.jcp.2011.06.003"> <button class="ui left aligned compact blue labeled icon button serp-button"> <i class="external alternate icon"></i> elsevier.com </button> </a> <a target="_blank" rel="external noopener" href="https://www.ncbi.nlm.nih.gov/pmc/articles/PMC3156558" title="pubmed link"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> pubmed.gov </button> </a>

Construction of Solenoidal Immersed Velocity Vectors Using the Kinematic Velocity--Vorticity Relation [article]

Fereidoun Sabetghadam, Shervin Sharafatmandjoor, Mehdi Badri
<span title="2012-04-09">2012</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The present paper suggests a method for obtaining incompressible solenoidal velocity vectors that satisfy approximately the desired immersed velocity boundary conditions.  ...  The method is applied to the two- and three-dimensional problems for the homogeneous Dirichlet, as well as periodic boundary conditions.  ...  Similar problem was observed in many other immersed boundary methods for the incompressible flow, and motivated emergence of some methods like the multi-direct forcing [22, 23] , or the implicit forcing  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.1916v1">arXiv:1204.1916v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/ltfvez3tovbjrlexezf3nv4pye">fatcat:ltfvez3tovbjrlexezf3nv4pye</a> </span>
<a target="_blank" rel="noopener" href="https://archive.org/download/arxiv-1204.1916/1204.1916.pdf" title="fulltext PDF download" data-goatcounter-click="serp-fulltext" data-goatcounter-title="serp-fulltext"> <button class="ui simple right pointing dropdown compact black labeled icon button serp-button"> <i class="icon ia-icon"></i> File Archive [PDF] </button> </a> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1204.1916v1" title="arxiv.org access"> <button class="ui compact blue labeled icon button serp-button"> <i class="file alternate outline icon"></i> arxiv.org </button> </a>

Cartesian Grid Method for Gas Kinetic Scheme [article]

Songze Chen, Kun Xu, Zhihui Li
<span title="2015-02-16">2015</span> <i > arXiv </i> &nbsp; <span class="release-stage" >pre-print</span>
The boundaries are represented by a set of direction-oriented boundary points. A constrained weighted least square method is employed to evaluate the physical quantities at the interpolation points.  ...  A few numerical examples are used to validate the Cartesian grid method and the simplified flux function.  ...  Their method applies the boundary condition on the immersed boundary to a high order by combining the ghost cell approach with a weighted least square error method based on a high order approximating polynomial  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener" href="https://arxiv.org/abs/1502.04494v1">arXiv:1502.04494v1</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/4tov4pnorncepafhvzywuwrlpe">fatcat:4tov4pnorncepafhvzywuwrlpe</a> </span>
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Kinematic and dynamic forcing strategies for predicting the transport of inertial capsules via a combined lattice Boltzmann – Immersed Boundary method

A. Coclite, S. Ranaldo, M.D. de Tullio, P. Decuzzi, G. Pascazio
<span title="">2019</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/wp3g5bo4ojczdinvl7cavuwkq4" style="color: black;">Computers &amp; Fluids</a> </i> &nbsp;
A Moving Least Squares (MLS) scheme has been implemented to correlate the pressure, velocity and force fields of the fluid domain with the capsule dynamics.  ...  Firstly, a combined Lattice Boltzmann-Immersed Boundary (LBM-IB) approach is developed for predicting the transport of inertial deformable capsules.  ...  obtained spreading ( ) into the support domain through a transferring equation, = ∑ Φ , where a moving least squares weighting rule is implemented [24, 55] . iv. is computed using Eq.(5) and of the previous  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1016/j.compfluid.2018.12.014">doi:10.1016/j.compfluid.2018.12.014</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/54yscbgldravzlc7kh7ttry3ou">fatcat:54yscbgldravzlc7kh7ttry3ou</a> </span>
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Influence of the Spool Velocity on The Performance of a Directional Hydraulic Valve

Antonio Posa, Paolo Oresta, Antonio Lippolis
<span title="">2013</span> <i title="Informa UK Limited"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/ycyjk5aqdze6pcpklqzqfpgusa" style="color: black;">International Journal of Fluid Power</a> </i> &nbsp;
phase of the valve has been solved by Direct Numerical Simulation (DNS), using an Immersed-Boundary (IB) technique.  ...  In this paper an accurate numerical method has been used to verify the influence of the spool velocity on the performance of a directional hydraulic valve (4/3, closed center): the flow during the opening  ...  The Immersed-boundary Method In the IB method the body is "immersed" into a regular grid, Cartesian or cylindrical: in general, no computational node is on the surface of the solid boundary, since the  ... 
<span class="external-identifiers"> <a target="_blank" rel="external noopener noreferrer" href="https://doi.org/10.1080/14399776.2013.10801410">doi:10.1080/14399776.2013.10801410</a> <a target="_blank" rel="external noopener" href="https://fatcat.wiki/release/lkz7bgvp2zfmzfwwushts7x23u">fatcat:lkz7bgvp2zfmzfwwushts7x23u</a> </span>
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