共查询到20条相似文献,搜索用时 609 毫秒
1.
A recent work of Li et al. [Numer. Math. Theor. Meth. Appl., 1(2008), pp.
92-112] proposed a finite volume solver to solve 2D steady Euler equations. Although
the Venkatakrishnan limiter is used to prevent the non-physical oscillations nearby the
shock region, the overshoot or undershoot phenomenon can still be observed. Moreover,
the numerical accuracy is degraded by using Venkatakrishnan limiter. To fix the
problems, in this paper the WENO type reconstruction is employed to gain both the
accurate approximations in smooth region and non-oscillatory sharp profiles near the
shock discontinuity. The numerical experiments will demonstrate the efficiency and
robustness of the proposed numerical strategy. 相似文献
2.
Although there is agreement that flexion and extension spaces should be symmetrical and that rotation of the femoral component impacts outcome in a knee replacement, there is dispute over what is the 'correct' rotation and how best to achieve it (Akagi et al., Clin Orthop Relat Res 366:155-163, 1999; Anouchi et al., Clin Orthop Relat Res 287:170-177, 1993; Barrack et al., Clin Orthop Relat Res 392:46-55, 2001; Berger et al., Clin Orthop Relat Res 356:144-153, 1998; Jenny and Boeri, Acta Orthop Scand 75(1):74-77, 2004; Poilvache et al., Clin Orthop Relat Res 331:35-46, 1996; Siston et al., J Bone Joint Surg Am 87(10):2276-2280, 2005). Insall and Scuderi recommended placing a tensor in flexion and rotating the femoral cutting block so that its posterior edge is parallel to the cut tibia (Insall, Surgery of the knee, vol 2, 2nd edn., Churchill Livingstone, New York, 1993; Scuderi and Insall, Orthop Clin N Am 20:71-78, 1989). We feel Equiflex instrumentation will reliably achieve Insall and Scuderi's recommendation. To evaluate early results and lateral retinacular release rates using Equiflex instrumentation for TKR, we evaluated 209 consecutive knees (31 valgus, 178 varus) using this technique from 4 April 2005 until 19 September 2006. Pre and postop American Knee Society and Oxford scores, deformity, ROM, lateral retinacular release rates and complications were recorded. We could correct alignment and achieve our technical goals in 99% of cases. A lateral retinacular release was required in only five knees (2.4%). The complications are comparable to published data. The Equiflex instrumentation does help in equalising flexion-extension gaps, improves patellar tracking and reduces the incidence of lateral retinacular release. 相似文献
3.
Adaptive Order WENO Reconstructions for the Semi-Lagrangian Finite Difference Scheme for Advection Problem 下载免费PDF全文
Jiajie Chen Xiaofeng Cai Jianxian Qiu & Jing-Mei Qiu 《Communications In Computational Physics》2021,30(1):67-96
We present a new conservative semi-Lagrangian finite difference weighted
essentially non-oscillatory scheme with adaptive order. This is an extension of the
conservative semi-Lagrangian (SL) finite difference WENO scheme in [Qiu and Shu,
JCP, 230 (4) (2011), pp. 863-889], in which linear weights in SL WENO framework
were shown not to exist for variable coefficient problems. Hence, the order of accuracy is not optimal from reconstruction stencils. In this paper, we incorporate a recent
WENO adaptive order (AO) technique [Balsara et al., JCP, 326 (2016), pp. 780-804]
to the SL WENO framework. The new scheme can achieve an optimal high order of
accuracy, while maintaining the properties of mass conservation and non-oscillatory
capture of solutions from the original SL WENO. The positivity-preserving limiter is
further applied to ensure the positivity of solutions. Finally, the scheme is applied to
high dimensional problems by a fourth-order dimensional splitting. We demonstrate
the effectiveness of the new scheme by extensive numerical tests on linear advection
equations, the Vlasov-Poisson system, the guiding center Vlasov model as well as the
incompressible Euler equations. 相似文献
4.
Numerical Solution of 3D Poisson-Nernst-Planck Equations Coupled with Classical Density Functional Theory for Modeling Ion and Electron Transport in a Confined Environment 下载免费PDF全文
Da Meng Bin Zheng Guang Lin & Maria L. Sushko 《Communications In Computational Physics》2014,16(5):1298-1322
We have developed efficient numerical algorithms for solving 3D steady-state
Poisson-Nernst-Planck (PNP) equations with excess chemical potentials described
by the classical density functional theory (cDFT). The coupled PNP equations are discretized
by a finite difference scheme and solved iteratively using the Gummel method
with relaxation. The Nernst-Planck equations are transformed into Laplace equations
through the Slotboom transformation. Then, the algebraic multigrid method is
applied to efficiently solve the Poisson equation and the transformed Nernst-Planck
equations. A novel strategy for calculating excess chemical potentials through fast
Fourier transforms is proposed, which reduces computational complexity from $\mathcal{O}$($N^2$) to $\mathcal{O}$($NlogN$), where $N$ is the number of grid points. Integrals involving the Dirac
delta function are evaluated directly by coordinate transformation, which yields more
accurate results compared to applying numerical quadrature to an approximated delta
function. Numerical results for ion and electron transport in solid electrolyte for lithium-ion
(Li-ion) batteries are shown to be in good agreement with the experimental data
and the results from previous studies. 相似文献
5.
In this paper, we present an adaptive moving mesh technique for solving
the incompressible viscous flows using the vorticity stream-function formulation. The
moving mesh strategy is based on the approach proposed by Li et al. [J. Comput. Phys.,
170 (2001), pp. 562–588] to separate the mesh-moving and evolving PDE at each time
step. The Navier-Stokes equations are solved in the vorticity stream-function form by
a finite-volume method in space, and the mesh-moving part is realized by solving the
Euler-Lagrange equations to minimize a certain variation in conjunction with a more
sophisticated monitor function. A conservative interpolation is used to redistribute
the numerical solutions on the new meshes. This paper discusses the implementation
of the periodic boundary conditions, where the physical domain is allowed to deform
with time while the computational domain remains fixed and regular throughout. Numerical results demonstrate the accuracy and effectiveness of the proposed algorithm. 相似文献
6.
A General Moving Mesh Framework in 3D and Its Application for Simulating the Mixture of Multi-Phase Flows 下载免费PDF全文
In this paper, we present an adaptive moving mesh algorithm for meshes
of unstructured polyhedra in three space dimensions. The algorithm automatically
adjusts the size of the elements with time and position in the physical domain to resolve the relevant scales in multiscale physical systems while minimizing computational costs. The algorithm is a generalization of the moving mesh methods based
on harmonic mappings developed by Li et al. [J. Comput. Phys., 170 (2001), pp. 562-588, and 177 (2002), pp. 365-393]. To make 3D moving mesh simulations possible,
the key is to develop an efficient mesh redistribution procedure so that this part will
cost as little as possible comparing with the solution evolution part. Since the mesh
redistribution procedure normally requires to solve large size matrix equations, we
will describe a procedure to decouple the matrix equation to a much simpler block-tridiagonal type which can be efficiently solved by a particularly designed multi-grid
method. To demonstrate the performance of the proposed 3D moving mesh strategy,
the algorithm is implemented in finite element simulations of fluid-fluid interface interactions in multiphase flows. To demonstrate the main ideas, we consider the formation of drops by using an energetic variational phase field model which describes
the motion of mixtures of two incompressible fluids. Numerical results on two- and
three-dimensional simulations will be presented. 相似文献
7.
Jonas Zeifang Jochen Schü tz Klaus Kaiser rea Beck & Sebastian Noelle 《Communications In Computational Physics》2020,27(1):292-320
In this paper, we introduce an extension of a splitting method for singularly
perturbed equations, the so-called RS-IMEX splitting [Kaiser et al., Journal of Scientific
Computing, 70(3), 1390–1407], to deal with the fully compressible Euler equations. The
straightforward application of the splitting yields sub-equations that are, due to the
occurrence of complex eigenvalues, not hyperbolic. A modification, slightly changing
the convective flux, is introduced that overcomes this issue. It is shown that the splitting gives rise to a discretization that respects the low-Mach number limit of the Euler
equations; numerical results using finite volume and discontinuous Galerkin schemes
show the potential of the discretization. 相似文献
8.
A Conservative and Monotone Characteristic Finite Element Solver for Three-Dimensional Transport and Incompressible Navier-Stokes Equations on Unstructured Grids 下载免费PDF全文
Bassou Khouya Mofdi El-Amrani & Mohammed Seaid 《Communications In Computational Physics》2022,31(1):224-256
We propose a mass-conservative and monotonicity-preserving characteristic finite element method for solving three-dimensional transport and incompressible
Navier-Stokes equations on unstructured grids. The main idea in the proposed algorithm consists of combining a mass-conservative and monotonicity-preserving modified method of characteristics for the time integration with a mixed finite element
method for the space discretization. This class of computational solvers benefits from
the geometrical flexibility of the finite elements and the strong stability of the modified method of characteristics to accurately solve convection-dominated flows using
time steps larger than its Eulerian counterparts. In the current study, we implement
three-dimensional limiters to convert the proposed solver to a fully mass-conservative
and essentially monotonicity-preserving method in addition of a low computational
cost. The key idea lies on using quadratic and linear basis functions of the mesh element where the departure point is localized in the interpolation procedures. The
proposed method is applied to well-established problems for transport and incompressible Navier-Stokes equations in three space dimensions. The numerical results
illustrate the performance of the proposed solver and support its ability to yield accurate and efficient numerical solutions for three-dimensional convection-dominated
flow problems on unstructured tetrahedral meshes. 相似文献
9.
A Pressure-Correction Scheme for Rotational Navier-Stokes Equations and Its Application to Rotating Turbulent Flows 下载免费PDF全文
Dinesh A. Shetty Jie Shen Abhilash J. Chandy & Steven H. Frankel 《Communications In Computational Physics》2011,9(3):740-755
The rotational incremental pressure-correction (RIPC) scheme, described in
Timmermans et al. [Int. J. Numer. Methods. Fluids., 22 (1996)] and Shen et al. [Math.
Comput., 73 (2003)] for non-rotational Navier-Stokes equations, is extended to rotating
incompressible flows. The method is implemented in the context of a pseudo
Fourier-spectral code and applied to several rotating laminar and turbulent flows.
The performance of the scheme and the computational results are compared to the so-called
diagonalization method (DM) developed by Morinishi et al. [Int. J. Heat. Fluid.
Flow., 22 (2001)]. The RIPC predictions are in excellent agreement with the DM predictions,
while being simpler to implement and computationally more efficient. The
RIPC scheme is not in anyway limited to implementation in a pseudo-spectral code or
periodic boundary conditions, and can be used in complex geometries and with other
suitable boundary conditions. 相似文献
10.
Background
The laparoscopic vertical sleeve gastrectomy (LSG) is derived from the biliopancreatic diversion with duodenal switch operation (Marceau et al., Obes Surg 3:29–35, 1993; Hess and Hess, Obes Surg 8:267–82, 1998; Chu et al., Surg Endosc 16:S069, 2002). Later, LSG was advocated as the first step of a two-stage procedure for super-obese patients (Regan et al., Obes Surg 13:861–4, 2003; Cottam et al., Surg Endosc 20:859–63, 2006). However, recent support is mounting that continues to establish LSG as the definitive procedure for surgical treatment of morbid obesity. We will report our experience with the LSG as a primary bariatric procedure and evaluate if this operation is suitable as a stand-alone procedure. 相似文献11.
A NURBS-Enhanced Finite Volume Method for Steady Euler Equations with Goal-Oriented $h$-Adaptivity 下载免费PDF全文
Xucheng Meng & Guanghui Hu 《Communications In Computational Physics》2022,32(2):490-523
In [A NURBS-enhanced finite volume solver for steady Euler equations, X. C.
Meng, G. H. Hu, J. Comput. Phys., Vol. 359, pp. 77–92], a NURBS-enhanced finite volume
method was developed to solve the steady Euler equations, in which the desired high
order numerical accuracy was obtained for the equations imposed in the domain with
a curved boundary. In this paper, the method is significantly improved in the following ways: (i) a simple and efficient point inversion technique is designed to compute
the parameter values of points lying on a NURBS curve, (ii) with this new point inversion technique, the $h$-adaptive NURBS-enhanced finite volume method is introduced
for the steady Euler equations in a complex domain, and (iii) a goal-oriented a posteriori
error indicator is designed to further improve the efficiency of the algorithm towards
accurately calculating a given quantity of interest. Numerical results obtained from a
variety of numerical experiments with different flow configurations successfully show
the effectiveness and robustness of the proposed method. 相似文献
12.
Shulin Wu Baochang Shi & Chengming Huang 《Communications In Computational Physics》2009,6(4):883-902
The parareal algorithm, proposed firstly by Lions et al. [J. L. Lions, Y. Maday,
and G. Turinici, A "parareal" in time discretization of PDE's, C.R. Acad. Sci.
Paris Sér. I Math., 332 (2001), pp. 661-668], is an effective algorithm to solve the time-dependent
problems parallel in time. This algorithm has received much interest from
many researchers in the past years. We present in this paper a new variant of the
parareal algorithm, which is derived by combining the original parareal algorithm
and the Richardson extrapolation, for the numerical solution of the nonlinear ODEs
and PDEs. Several nonlinear problems are tested to show the advantage of the new
algorithm. The accuracy of the obtained numerical solution is compared with that of
its original version (i.e., the parareal algorithm based on the same numerical method). 相似文献
13.
《Seminars in spine surgery》2019,31(3):100708
Originally described by Kirkaldy–Willis, the degenerative cascade leading to anatomic LSS occurs in a predictable pattern, beginning with altered biomechanics of the intervertebral disk (Yong-Hing and Kirkaldy-Willis, 1983). Further studies have elucidated several theorized mechanisms responsible for the varied clinical manifestations experienced by patients with similar radiographic evidence of LSS; however, a single explanation for these finding has yet to be identified (Olemarker et al., 1996; Rydevick et al., 1991; Pedowitz et al., 1992). Obtaining thorough patient history and performing a complete physical exam is critical to ensure an accurate diagnosis. Although neurogenic claudication symptoms are classic for LSS, patients frequently present with varied and often mixed symptomatology (Buckland et al, 2017; Lesher et al., 2008). Consistent screening for myelopathic symptoms, identifying “red-flag” symptoms suggesting systemic illness, and awareness of potential extraspinal pathology is necessary to improve patient outcomes (Devin et al, 2012; Golob et al, 2006; Berger et al, 2017). 相似文献
14.
This paper presents a modeling framework—mathematical model and computational framework—to study the response of a plastic material due to the presence
and transport of a chemical species in the host material. Such a modeling framework
is important to a wide variety of problems ranging from Li-ion batteries, moisture
diffusion in cementitious materials, hydrogen diffusion in metals, to consolidation of
soils under severe loading-unloading regimes. The mathematical model incorporates
experimental observations reported in the literature on how (elastic and plastic) material properties change because of the presence and transport of a chemical species.
Also, the model accounts for one-way (transport affects the deformation but not vice
versa) and two-way couplings between deformation and transport subproblems. The
resulting coupled equations are not amenable to analytical solutions; so, we present a
robust computational framework for obtaining numerical solutions. Given that popular numerical formulations do not produce nonnegative solutions, the computational
framework uses an optimized-based nonnegative formulation that respects physical
constraints (e.g., nonnegative concentrations). For completeness, we also show the
effect and propagation of the negative concentrations, often produced by contemporary transport solvers, into the overall predictions of deformation and concentration
fields. Notably, anisotropy of the diffusion process exacerbates these unphysical violations. Using representative numerical examples, we discuss how the concentration
field affects plastic deformations of a degrading solid. Based on these numerical examples, we also discuss how plastic zones spread because of material degradation.
To illustrate how the proposed computational framework performs, we report various
performance metrics such as optimization iterations and time-to-solution. 相似文献
15.
Borisch N Lerch K Grifka J Haussmann P 《The Journal of hand surgery, European volume》2004,29(2):144-147
The indices for ulnar translation described by Chamay et al. (1983, Annales de Chirurgie de la Main, Vol. 2, pp. 5-17), and Bouman et al. (1994, Journal of Hand Surgery Vol. 19B, pp. 325-329), and for carpal height described by Youm et al. (1978, Journal of Bone and Joint Surgery, Vol. 40A, pp. 423-431) and Bouman et al. (1994) were compared in pre- and postoperative wrist X-rays of 91 patients with rheumatoid arthritis undergoing radiolunate arthrodesis. Both indices described by Bouman had a higher applicability and sensitivity than the Chamay and Youm indices and are recommended for use with the rheumatoid wrist. However false-negative values may result when the Bouman index for ulnar translation is used to follow up radiolunate arthrodesis. 相似文献
16.
In this paper, we are concerned with probabilistic high order numerical
schemes for Cauchy problems of fully nonlinear parabolic PDEs. For such parabolic
PDEs, it is shown by Cheridito, Soner, Touzi and Victoir [4] that the associated exact
solutions admit probabilistic interpretations, i.e., the solution of a fully nonlinear
parabolic PDE solves a corresponding second order forward backward stochastic differential
equation (2FBSDEs). Our numerical schemes rely on solving those 2FBSDEs,
by extending our previous results [W. Zhao, Y. Fu and T. Zhou, SIAM J. Sci. Comput.,
36 (2014), pp. A1731-A1751.]. Moreover, in our numerical schemes, one has the flexibility
to choose the associated forward SDE, and a suitable choice can significantly
reduce the computational complexity. Various numerical examples including the HJB
equations are presented to show the effectiveness and accuracy of the proposed numerical
schemes. 相似文献
17.
Computational Investigation of the Effects of Sample Geometry on the Superconducting-Normal Phase Boundary and Vortex-Antivortex States in Mesoscopic Superconductors 下载免费PDF全文
Sangbum Kim Max Gunzburger Janet Peterson & Chia-Ren Hu 《Communications In Computational Physics》2009,6(4):673-698
A computational study of superconducting states near the superconducting-normal
phase boundary in mesoscopic finite cylinders is presented. The computational
approach uses a finite element method to find numerical solutions of the linearized
Ginzburg-Landau equation for samples with various sizes, aspect ratios, and cross-sectional
shapes, i.e., squares, triangles, circles, pentagons, and four star shapes. The
vector potential is determined using a finite element method with two penalty terms
to enforce the gauge conditions that the vector potential is solenoidal and its normal
component vanishes at the surface(s) of the sample. The eigenvalue problem for the
linearized Ginzburg-Landau equations with homogeneous Neumann boundary conditions
is solved and used to construct the superconducting-normal phase boundary
for each sample. Vortex-antivortex (V-AV) configurations for each sample that accurately
reflect the discrete symmetry of each sample boundary were found through the
computational approach. These V-AV configurations are realized just within the phase
boundary in the magnetic field-temperature phase diagram. Comparisons are made
between the results obtained for the different sample shapes. 相似文献
18.
In this work, we propose an efficient multi-mesh adaptive finite element
method for simulating the dendritic growth in two- and three-dimensions. The governing equations used are the phase field model, where the regularity behaviors of the
relevant dependent variables, namely the thermal field function and the phase field
function, can be very different. To enhance the computational efficiency, we approximate these variables on different h-adaptive meshes. The coupled terms in the system
are calculated based on the implementation of the multi-mesh h-adaptive algorithm
proposed by Li (J. Sci. Comput., pp. 321-341, 24 (2005)). It is illustrated numerically
that the multi-mesh technique is useful in solving phase field models and can save
storage and the CPU time significantly. 相似文献
19.
A fourth-order finite difference method is proposed and studied for the
primitive equations (PEs) of large-scale atmospheric and oceanic flow based on mean
vorticity formulation. Since the vertical average of the horizontal velocity field is
divergence-free, we can introduce mean vorticity and mean stream function which are
connected by a 2-D Poisson equation. As a result, the PEs can be reformulated such that
the prognostic equation for the horizontal velocity is replaced by evolutionary equations for the mean vorticity field and the vertical derivative of the horizontal velocity.
The mean vorticity equation is approximated by a compact difference scheme due to
the difficulty of the mean vorticity boundary condition, while fourth-order long-stencil
approximations are utilized to deal with transport type equations for computational
convenience. The numerical values for the total velocity field (both horizontal and
vertical) are statically determined by a discrete realization of a differential equation at
each fixed horizontal point. The method is highly efficient and is capable of producing highly resolved solutions at a reasonable computational cost. The full fourth-order
accuracy is checked by an example of the reformulated PEs with force terms. Additionally, numerical results of a large-scale oceanic circulation are presented. 相似文献
20.
Shizhao Wang Xing Zhang & Guowei He 《Communications In Computational Physics》2012,11(4):1323-1333
The swimming of a 3D fish-like body with finlets is numerically investigated
at Re = 1000 (the Reynolds number is based on the uniform upstream flow and the
length of the fish-like body). The finlets are simply modeled as thin rigid rectangular
plates that undulate with the body. The wake structures and the flow around the caudal peduncle are studied. The finlets redirect the local flow across the caudal peduncle
but the vortical structures in the wake are almost not affected by the finlets. Improvement of hydrodynamic performance has not been found in the simulation based on
this simple model. The present numerical result is in agreement with that of the work
of Nauen and Lauder [J. Exp. Biol., 204 (2001), pp. 2251-2263] and partially supports
the hypothesis of Webb [Bull. Fish. Res. Bd. Can., 190 (1975), pp. 1-159]. 相似文献