Additive Schwarz Preconditioners with Minimal Overlap for Triangular Spectral Elements

The additive Schwarz preconditioner with minimal overlap is extended to triangular spectral elements (TSEM). The method is a generalization of the corresponding method in tensorial quadrilateral spectral elements (QSEM). The proposed preconditioners are based on partitioning the domain into overlapping subdomains, solving local problems on these subdomains and solving an additional coarse problem associated with the subdomain mesh. The results of numerical experiments show that the proposed preconditioner are robust with respect to the number of elements and are more efficient than the preconditioners with generous overlaps.     

A Priori Subcell Limiting Approach for the FR/CPR Method on Unstructured Meshes

A priori subcell limiting approach is developed for high-order flux reconstruction/correction procedure via reconstruction (FR/CPR) methods on two-dimensional unstructured quadrilateral meshes. Firstly, a modified indicator based on modal energy coefficients is proposed to detect troubled cells, where discontinuities exist. Then, troubled cells are decomposed into nonuniform subcells and each subcell has one solution point. A second-order finite difference shock-capturing scheme based on nonuniform nonlinear weighted (NNW) interpolation is constructed to perform the calculation on troubled cells while smooth cells are calculated by the CPR method. Numerical investigations show that the proposed subcell limiting strategy on unstructured quadrilateral meshes is robust in shock-capturing.     

A Spectral Element Implementation for the M3D Extended MHD Code

A spectral element library has been developed and integrated with the M3D extended MHD code. The currently used linear triangular finite element implementation and the new high order quadrilateral spectral element implementation are directly compared on equilibrium, linear stability, and nonlinear evolution calculations run on the same problems.     

An Optimized Correction Procedure via Reconstruction Formulation for Broadband Wave Computation

Recently, a new differential discontinuous formulation for conservation laws named the Correction Procedure via Reconstruction (CPR) is developed, which is inspired by several other discontinuous methods such as the discontinuous Galerkin (DG), the spectral volume (SV)/spectral difference (SD) methods. All of them can be unified under the CPR formulation, which is relatively simple to implement due to its finite-difference-like framework. In this paper, a different discontinuous solution space including both polynomial and Fourier basis functions on each element is employed to compute broad-band waves. Free-parameters introduced in the Fourier bases are optimized to minimize both dispersion and dissipation errors through a wave propagation analysis. The optimization procedure is verified with a mesh resolution analysis. Numerical results are presented to demonstrate the performance of the optimized CPR formulation.     

A Class of Hybrid DG/FV Methods for Conservation Laws III: Two-Dimensional Euler Equations

A concept of "static reconstruction" and "dynamic reconstruction" was introduced for higher-order (third-order or more) numerical methods in our previous work. Based on this concept, a class of hybrid DG/FV methods had been developed for one-dimensional conservation law using a "hybrid reconstruction" approach, and extended to two-dimensional scalar equations on triangular and Cartesian/triangular hybrid grids. In the hybrid DG/FV schemes, the lower-order derivatives of the piecewise polynomial are computed locally in a cell by the traditional DG method (called as "dynamic reconstruction"), while the higher-order derivatives are reconstructed by the "static reconstruction" of the FV method, using the known lower-order derivatives in the cell itself and in its adjacent neighboring cells. In this paper, the hybrid DG/FV schemes are extended to two-dimensional Euler equations on triangular and Cartesian/triangular hybrid grids. Some typical test cases are presented to demonstrate the performance of the hybrid DG/FV methods, including the standard vortex evolution problem with exact solution, isentropic vortex/weak shock wave interaction, subsonic flows past a circular cylinder and a three-element airfoil (30P30N), transonic flow past a NACA0012 airfoil. The accuracy study shows that the hybrid DG/FV method achieves the desired third-order accuracy, and the applications demonstrate that they can capture the flow structure accurately, and can reduce the CPU time and memory requirement greatly than the traditional DG method with the same order of accuracy.     

High-Order Conservative Asymptotic-Preserving Schemes for Modeling Rarefied Gas Dynamical Flows with Boltzmann-BGK Equation

High-order and conservative phase space direct solvers that preserve the Euler asymptotic limit of the Boltzmann-BGK equation for modelling rarefied gas flows are explored and studied. The approach is based on the conservative discrete ordinate method for velocity space by using Gauss Hermite or Simpsons quadrature rule and conservation of macroscopic properties are enforced on the BGK collision operator. High-order asymptotic-preserving time integration is adopted and the spatial evolution is performed by high-order schemes including a finite difference weighted essentially non-oscillatory method and correction procedure via reconstruction schemes. An artificial viscosity dissipative model is introduced into the Boltzmann-BGK equation when the correction procedure via reconstruction scheme is used. The effects of the discrete velocity conservative property and accuracy of high-order formulations of kinetic schemes based on BGK model methods are provided. Extensive comparative tests with one-dimensional and two-dimensional problems in rarefied gas flows have been carried out to validate and illustrate the schemes presented. Potentially advantageous schemes in terms of stable large time step allowed and higher-order of accuracy are suggested.     

Arbitrary-Lagrangian-Eulerian One-Step WENO Finite Volume Schemes on Unstructured Triangular Meshes

In this article we present a new class of high order accurate ArbitraryEulerian-Lagrangian (ALE) one-step WENO finite volume schemes for solving nonlinear hyperbolic systems of conservation laws on moving two dimensional unstructured triangular meshes. A WENO reconstruction algorithm is used to achieve high order accuracy in space and a high order one-step time discretization is achieved by using the local space-time Galerkin predictor proposed in [25]. For that purpose, a new element-local weak formulation of the governing PDE is adopted on moving space-time elements. The space-time basis and test functions are obtained considering Lagrange interpolation polynomials passing through a predefined set of nodes. Moreover, a polynomial mapping defined by the same local space-time basis functions as the weak solution of the PDE is used to map the moving physical space-time element onto a space-time reference element. To maintain algorithmic simplicity, the final ALE one-step finite volume scheme uses moving triangular meshes with straight edges. This is possible in the ALE framework, which allows a local mesh velocity that is different from the local fluid velocity. We present numerical convergence rates for the schemes presented in this paper up to sixth order of accuracy in space and time and show some classical numerical test problems for the two-dimensional Euler equations of compressible gas dynamics.     

Quadrilateral Cell-Based Anisotropic Adaptive Solution for the Euler Equations

An anisotropic solution adaptive method based on unstructured quadrilateral meshes for inviscid compressible flows is proposed. The data structure, the directional refinement and coarsening, including the method for initializing the refined new cells, for the anisotropic adaptive method are described. It provides efficient high resolution of flow features, which are aligned with the original quadrilateral mesh structures. Five different cases are provided to show that it could be used to resolve the anisotropic flow features and be applied to model the complex geometry as well as to keep a relative high order of accuracy on an efficient anisotropic mesh.     

A Third Order Conservative Lagrangian Type Scheme on Curvilinear Meshes for the Compressible Euler Equations

Based on the high order essentially non-oscillatory (ENO) Lagrangian type scheme on quadrilateral meshes presented in our earlier work [3], in this paper we develop a third order conservative Lagrangian type scheme on curvilinear meshes for solving the Euler equations of compressible gas dynamics. The main purpose of this work is to demonstrate our claim in [3] that the accuracy degeneracy phenomenon observed for the high order Lagrangian type scheme is due to the error from the quadrilateral mesh with straight-line edges, which restricts the accuracy of the resulting scheme to at most second order. The accuracy test given in this paper shows that the third order Lagrangian type scheme can actually obtain uniformly third order accuracy even on distorted meshes by using curvilinear meshes. Numerical examples are also presented to verify the performance of the third order scheme on curvilinear meshes in terms of resolution for discontinuities and non-oscillatory properties.     

Monotonicity Correction for the Finite Element Method of Anisotropic Diffusion Problems

We apply the monotonicity correction to the finite element method for the anisotropic diffusion problems, including linear and quadratic finite elements on triangular meshes. When formulating the finite element schemes, we need to calculate the integrals on every triangular element, whose results are the linear combination of the two-point pairs. Then we decompose the integral results into the main and remaining parts according to coefficient signs of two-point pairs. We apply the nonlinear correction to the positive remaining parts and move the negative remaining parts to the right side of the finite element equations. Finally, the original stiffness matrix can be transformed into a nonlinear M-matrix, and the corrected schemes have the positivity-preserving property. We also give the monotonicity correction to the time derivative term for the time-dependent problems. Numerical experiments show that the corrected finite element method has monotonicity and maintains the convergence order of the original schemes in $H^1$-norm and $L^2$-norm, respectively.     

髋臼四方区复杂型骨折手术入路的选择

目的：根据复杂型髋臼四方区骨折的不同类型,探讨不同手术入路,以获得更好的手术暴露和更可靠的复住内固定。方法：自2006年1月至2011年1月共收治58例髋臼四方区骨折,男36例,女22例;年龄23～61岁,平均36．9岁。术前摄骨盆片及双斜位片,辅以CT扫描重建髋臼,按Letournel分型其中前柱15例,横形12例,T形7例,前柱伴后半横形9例,双柱骨折15例。分别采用单纯Kocher—Langenbeck（K—L）入路、髂腹股沟入路、改良的Stoppa入路手术、组合式联合手术入路,或者经改良Stoppa入路结合经皮髋臼前柱拉力螺钉固定。结果：49例患者获随访,时间2～6年,平均32个月,术后其中1例发生深部感染,经创口引流,配合有效抗生素后治愈,2例出现坐骨神经损伤,2例出现股骨头坏死。手术结果复位按Matta标准评定：解剖复位（移位〈1mm）36例,满意复位（移位1～3mm）8例,不满意复位（移位〉3ram）5例。关节功能按Merle d＇Aubigne和Postel标准评定：优32例,良12例,可4例,差1倒,总分（15．3±2．5）。结论：采用单一的手术入路只能解决一部分类型的髋臼复杂型四方区骨折,更多的需要采用联合入路,改良的Stoppa入路结合髂腹股沟前入路或者结合前柱髋臼螺钉通常是解决复杂型四方区骨折移位有效的手术入路,临床疗效满意。     

Rationales for the Bernese approaches in acetabular surgery

Purpose

To present two new approaches to acetabular surgery that were established in Berne, and which aim at enhanced visualization and anatomical reconstruction of acetabular fractures.

Method

The trochanteric flip osteotomy allows for surgical hip dislocation, and was introduced as a posterior approach for acetabular fracture management involving the posterior column and wall. For acetabular fractures predominantly involving the anterior column and the quadrilateral plate, the Pararectus approach is described.

Results

Full exposure of the hip joint, as provided by the trochanteric flip osteotomy, facilitates anatomical reduction of acetabular or femoral head fractures and safe positioning of the anterior column screw in transverse or T-shaped fractures. Additionally, the approach enables osteochondral transplantation as a salvage procedure for severe chondral femoral head damage and osteoplasty of an associated inadequate offset at the femoral head–neck junction. The Pararectus approach allows anatomical restoration with minimal access morbidity, and combines advantages of the ilioinguinal and modified Stoppa approaches.

Conclusions

Utilization of the trochanteric flip osteotomy eases visualization of the superior aspect of the acetabulum, and enables the evaluation and treatment of chondral lesions of the femoral head or acetabulum and labral tears. Displaced fractures of the anterior column with a medialized quadrilateral plate can be addressed successfully through the Pararectus approach, in which surgical access is associated with minimal morbidity. However, long-term results following the two presented Bernese approaches are needed to confirm that in the treatment of complex acetabular fractures the rate of poor results in almost one-third of all cases (as currently yielded using traditional approaches) might be reduced by the utilization of the presented novel approaches.     

Improving the High Order Spectral Volume Formulation Using a Diffusion Regulator

The concept of diffusion regulation (DR) was originally proposed by Jaisankar for traditional second order finite volume Euler solvers. This was used to decrease the inherent dissipation associated with using approximate Riemann solvers. In this paper, the above concept is extended to the high order spectral volume (SV) method. The DR formulation was used in conjunction with the Rusanov flux to handle the inviscid flux terms. Numerical experiments were conducted to compare and contrast the original and the DR formulations. These experiments demonstrated (i) retention of high order accuracy for the new formulation, (ii) higher fidelity of the DR formulation, when compared to the original scheme for all orders and (iii) straightforward extension to Navier Stokes equations, since the DR does not interfere with the discretization of the viscous fluxes. In general, the 2D numerical results are very promising and indicate that the approach has a great potential for 3D flow problems.     

Two-Relaxation-Time Lattice Boltzmann Scheme: About Parametrization,Velocity, Pressure and Mixed Boundary Conditions

We develop a two-relaxation-time (TRT) Lattice Boltzmann model for hydrodynamic equations with variable source terms based on equivalent equilibrium functions. A special parametrization of the free relaxation parameter is derived. It controls, in addition to the non-dimensional hydrodynamic numbers, any TRT macroscopic steady solution and governs the spatial discretization of transient flows. In this framework, the multi-reflection approach [16, 18] is generalized and extended for Dirichlet velocity, pressure and mixed (pressure/tangential velocity) boundary conditions. We propose second- and third-order accurate boundary schemes and adapt them for corners. The boundary schemes are analyzed for exactness of the parametrization, uniqueness of their steady solutions, support of staggered invariants and for the effective accuracy in case of time dependent boundary conditions and transient flow. When the boundary scheme obeys the parametrization properly, the derived permeability values become independent of the selected viscosity for any porous structure and can be computed efficiently. The linear interpolations [5, 46] are improved with respect to this property.     

The devices used to correct the urinary incontinence by tension-free meshes. Are all them equals?

Since 1996, when Ulmsten described the TVT procedure (Tension-free Vaginal Tape) for correction of women urinary stress incontinence, a large number of different devices have been manufactured with that purpose. Results depend not only of the surgical procedure but also of two principal factors: 1. Characteristics and properties of the mesh. 2. System and way for the implantation. Properties of the mesh used are probably as important as surgical technique. It's not possible to assume that results achieved with the TVT device will be similar with other meshes. Further randomized studies will be necessary to make these affirmations. In this paper we analyse properties of the mesh, characteristics of the implantation system and the influence of those factors in the surgical results. Finally, we describe some of the devices available and the mesh characteristics of each one.     

Primary Issues in the Selection of Surgical Procedures for Thoracic and Lumbar Spinal Tuberculosis

Debridement, spinal canal decompression, deformity correction, bone graft fusion and internal fixation are commonly used in the surgical treatment of spinal tuberculosis. A complete surgical plan for patients with spinal tuberculosis may include all or some of these five surgical procedures that involve both removing tuberculous lesions and re‐establishing spinal stability and function. All five procedures can be carried out via an anterior or posterior approach or a combination of these two approaches. A combined posterior–anterior approach is becoming a preferred choice for treating spinal tuberculosis. However, this procedure requires two incisions and two rounds of surgeries, which the associated extensive surgical trauma. Thus, a simple anterior or posterior approach may be preferable. Each of these approaches has its own advantages and disadvantages that must be considered during the clinician's evaluation. Selection of the most appropriate of these three approaches is vital to achieving cure of spinal tuberculosis. Spinal surgeons should comprehensively consider each patient's characteristics, the manifestations of their lesions and how familiar the surgeon is with the required surgical procedure(s). The primary consideration should be the potential outcome: the effectiveness of debridement is the key determinant of the surgical outcome.     

Recurrent perineal hernia repair: a novel approach

Purpose

Postoperative perineal hernias are rare complications from procedures, which compromise the pelvic floor, mainly abdominoperineal resection, proctocolectomy, and partial or total pelvic exenteration. Surgical repair can be accomplished through abdominal, laparoscopic, or transperineal approaches.

Methods

We present a case report of a 70-year-old man who underwent two prior operations for recurrent perineal hernia and was ultimately successfully treated with a third operation, a synthetic mesh redo procedure that utilized a synthetic mesh system marketed for women with pelvic organ prolapse.

Results

Although there is no "gold standard" for perineal hernia repair, our patient had multiple surgeries employing a variety of approaches. Final success was achieved using a mesh system with improved fixation to secure pelvic ligaments, using an exclusive perineal approach. Now, more than five years following the final surgery, the patient remains symptom free with no clinical evidence of perineal hernia recurrence.

Conclusions

To date, this is the only report of using this mesh system in a male. The advantages of using this mesh system are (1) exclusive perineal approach without the accompanying risks of abdominal or laparoscopic approach; (2) improved fixation of mesh to secure pelvic ligaments; and (3) lightweight, flexible, and large mesh shape that can easily be trimmed to allow versatility in procedures.     

Combining colposacropexy and Ripstein procedure for combined vaginal vault and rectal prolapse: With and without retropubic colpourethropexy for stress urinary incontinence

The literature concerning the concurrent surgical correction for coexisting posthysterectomy vault and intussuscepting rectal prolapse is reviewed. Only two such papers have been published in the past, reporting a total of three cases. Five such cases and their surgical correction using Marlex mesh for both modified Ripstein procedure and colposacropexy are presented. The need for thorough preoperative urodynamic evaluation and defecography is discussed. All patients had good anatomic correction of their genital and rectal prolapse in follow-up. One patient, who had a prior retropubic urethropexy only, was treated by a combined Ripstein and colposacropexy and postoperatively developed recurrent stress urinary incontinence as a consequence of overcorrection by the colposacropexy. This was subsequently corrected by a combined abdominovaginal Marlex mesh sling procedure. There were no operative or postoperative complications, and it is concluded that, in the hands of experienced surgeons, colposacropexy and Ripstein procedure for combined vaginal vault and rectal prolapse can be a safe and effective treatment.