A spectral dual mesh control domain framework for nonlinear fluid flow and coupled multi-field problems

Traumatic lumbar hernia (TLH) is a rare and challenging abdominal wall defect. In these patients, treatment success is usually assessed by recurrence, although persistent postoperative bulging or asymmetry may remain clinically relevant even without true failure of repair. This study evaluated the abdominal symmetry index (ASI), defined as a CT-based side-to-side ratio of lateral abdominal wall distance, as an objective morphologic parameter after TLH reconstruction with dual polypropylene mesh. A single-center retrospective comparative study was performed at a tertiary academic referral center from 2006 to 2025. The study included 25 consecutive eligible patients with TLH who underwent elective open abdominal wall reconstruction with dual polypropylene mesh and 25 controls without abdominal wall disease. In the TLH group, ASI was assessed on CT before and after surgery; controls underwent a single CT-based assessment. The operative repair consisted of deep preperitoneal/retroperitoneal reinforcement whenever feasible, muscle reapproximation when possible, and preaponeurotic/onlay reinforcement. Sex distribution did not differ significantly between groups. Mean age was 42 +/- 13 years in the hernia group and 37 +/- 13 years in controls, while mean body mass index was 31 +/- 4 and 28 +/- 5kg/m2, respectively (p = 0.023). Hernia volume was estimated using the ellipsoid formula and had a median value of 443 cm3 (range, 244-1013 cm3). Clinical follow-up was 62 +/- 47 months, and the interval between surgical repair and the latest postoperative CT scan was 687.3 +/- 712.6 days. No recurrence was observed. Before surgery, the measurement on the hernia side was significantly greater than on the contralateral side (185 +/- 24mm vs. 144 +/- 12mm; p < 0.0001). After reconstruction, this difference was no longer statistically significant (154 +/- 15mm vs. 149 +/- 13mm; p = 0.1022). Mean ASI was 1.29 +/- 0.18 preoperatively, 1.03 +/- 0.07 postoperatively, and 0.99 +/- 0.03 in controls (overall p < 0.0001). Holm-Sidak adjusted pairwise comparisons showed significant differences between preoperative TLH and controls (p = 1.14 × 10^-13) and between preoperative and postoperative TLH (p = 1.64 × 10^-11), whereas postoperative TLH did not differ significantly from controls (p = 0.2142). ASI was feasible as an exploratory CT-based morphologic index for postoperative evaluation of TLH repair. Reconstruction with dual polypropylene mesh was associated with substantial improvement in abdominal wall symmetry, with postoperative values approaching those of controls. Further validation, including interobserver reproducibility and correlation with patient-reported outcomes, is required before broader adoption.

Trifecta Outcomes after Robotic Sacrocolpopexy with Dual Mesh in Single-center Cohort.

The purpose of this paper is to discuss the notion of conservation in hyperbolic systems and how one can formulate it at the discrete level depending on the representation of the solution on the mesh. Since it is impossible to have a fully general theory, we discuss several alternatives possibilities: cases where the solution is represented by average in volumes; cases where the mesh is staggerred (i.e. the components of the solution are not localized at the same places); cases where the solution is solely represented by point values; and an example where all the previous options are mixed. We show how each configuration can provide, or not, enough flexibility. Though the discussion could be adapted to any hyperbolic system endowed with an entropy, we focus on compressible fluid mechanics, it its Eulerian and Lagrangian formulations. On a given mesh, the unifying element is that we systematically express the update of conserved variables as [Formula: see text], where the functional [Formula: see text] depends on the value of [Formula: see text] at the current degree of freedom and its values from a set of degrees of freedom. This set defines the stencil of the scheme. From the stencil, one can naturally define a graph connecting the states that appears in [Formula: see text]. The notion of local conservation can be defined from this graph. We are aware of only two possible situations: either the graph is constructed from the faces of the mesh elements (or the dual mesh), or it is defined from the mesh itself. Two notions of local conservation then emerge: either we define a numerical flux, or we define a “residual” attached to elements and the degrees of freedom within the element. We show that this two notions are in a way equivalent, but the one with residual allows much more flexibility, especially if additional algebraic constraints must be satisfied. Examples of specific additional conservation constraints are provided to illustrate this flexibility. We also show that this notion of conservation gives a very clear framework for the design of schemes in the Lagrangian setting. In the ending section, we will provide a number of ongoing research avenues strongly related to the formulation discussed, and we highlight some open questions which will be explored in the future.

Pelvic organ prolapse (POP) is frequently encountered in elderly women. However, it can also affect relatively young women of reproductive age. Here, we present three cases of uterine-sparing robot-assisted sacrocolpopexy (RSC) in women aiming for pregnancy. All cases were diagnosed with POP-Q stage III. Utilizing the da Vinci X or Xi robotic surgical system, they underwent uterine-sparing RSC with dual mesh anterior and posterior walls. The anterior wall mesh was not a Y-shaped mesh encircling the cervix; The anterior wall mesh was not a Y-shaped mesh encircling the cervix; rather, it was placed only through the window of the right broad ligament to minimize uterine artery compression caused by the mesh. No perioperative complications or short-term recurrences were noted. Uterine-sparing robotic-assisted sacrocolpopexy represents a valuable surgical option for patients with POP who wish to become pregnant.

A dual solar-utilization photocatalytic mesh reactor for efficient harmful algal bloom control in real-world conditions: Performance, mechanism and global deployment

Bending and vibration analyses of functionally graded auxetic doubly curved shells via dual mesh control domain model

Carrier-based aircraft recovery is a critical and challenging phase in maritime operations due to the turbulent airwake generated by aircraft carriers, which significantly increases the workload of flight control systems and pilots. This study investigates the airwake effects of an aircraft carrier under varying wind direction conditions. A high-fidelity mathematical model combining delayed detached-eddy simulation (DDES) with the overset grid method was developed to analyze key flow characteristics, including upwash, downwash, and lateral recirculation. The model ensures precise control of aircraft speed and trajectory during landing while maintaining numerical stability through rigorous mesh optimization. The results indicate that the minimum lift occurs in the downwash region aft of the deck, marking it as the most hazardous zone during landing. Aircraft above the deck are primarily influenced by ground effects, causing a sudden increase in lift that complicates arresting wire engagement. Additionally, the side force on the aircraft undergoes an abrupt reversal during the approach phase. The dual overset mesh technique effectively captures the coupled motion of the hull and aircraft, revealing higher turbulence intensity along the glideslope and a wider range of lift fluctuations compared to stationary hull conditions. These findings provide valuable insights for optimizing carrier-based aircraft recovery procedures, offering more realistic data for simulation training and enhancing pilot preparedness for airwake-induced disturbances.

Abstract Three types of lowest-order finite volume element methods, i.e., the conforming, nonconforming and discontinuous schemes, are introduced and analysed for a variational inequality governed by the stationary Stokes equations. The variational inequality arises due to a nonlinear and nondifferentiable relationship in the slip boundary condition of friction type. This relationship cannot be well combined into a finite volume scheme by a standard procedure based on integration by parts on dual control volumes. Thereby we propose to enforce it pointwisely at cell centres in a dual mesh, which leads to some numerical integration formula for the boundary nonlinear term in the variational inequality. The resulting finite volume schemes can be seen to be equivalent to some finite element methods. We further show their solvability and stability, as well as the a priori error estimates with optimal approximation behaviours. Numerical results are reported to demonstrate the theoretical findings.

Abstract INTRODUCTION: The development of post-operative abdominal compartment syndrome is one of the major risks associated with the repair of massive parastomal hernias. Minimizing the occurrence of such post-operative complications is imperative but challenging. Plastic surgery techniques in complex hernia repairs can offer significant advantages in such complex surgeries. CASE PRESENTATION: We present a case of a 26-year-old, obese, non-smoking male with a massive left-sided parastomal hernia extending below the inguinal region. The hernia was confirmed on a pre-operative computed tomography (CT) and seen to include most of the remaining bowel area. Pre-operative optimization of the abdominal wall was performed by ultrasound-guided botulinum toxin injections to all three abdominal wall muscles bilaterally. The surgery was performed in three steps involving the reduction of the hernia, abdominal wall component separation, closure of the abdominal wall with dual mesh placement, de-epithelization and folding of excess abdominal skin, and repositioning of the stoma. Post-operatively, the patient was followed-up for pain, ventilatory problems, and increasing abdominal pressures. CONCLUSION: Massive parastomal hernia repair avoiding post-operative abdominal compartment syndrome can be achieved by application of a multi-dimensional surgical approach. The use of pre-operative Botox represents an innovative approach that may reduce the risk of post-operative complications.

Abstract This paper presents the novel Isogeometric Finite Volume Method (IGFVM) for the numerical solution of steady-state heat transfer problems. The method utilizes the finite volume method (FVM) to derive integral balance equations over control volumes and Isogeometric analysis (IGA) to represent the solution field, resulting in an accurate representation of the problem’s geometry. The proposed approach is based on a dual mesh representation: the first mesh is used for the geometry and solution field, and the second mesh is used for the control volume discretization. NURBS-based representations are employed for the geometry and solution mesh. The control volume mesh is generated based on the geometry mesh, enabling the balance equations to be applied precisely on control volumes that exactly replicate the geometry. This eliminates inconsistencies between the problem’s geometry and the analysis model. The results demonstrate the validity of the proposed formulation and its capability to bridge the gap between accurate geometric representations of complex domains and numerical analysis. Furthermore, the use of NURBS enables easy incorporation of higher polynomial degrees, supporting solution fields with high continuity. Numerical studies on one and two-dimensional problems are presented, along with a comparison to the well-established Galerkin Isogeometric Analysis (IGA). A representative MATLAB implementation is provided as supplementary material. The results demonstrate the validity of the proposed formulation and its capability to bridge the gap between accurate geometric representations of complex domains and numerical analysis.

Background: Preventing lung herniation and maintaining a stable thoracic cage remain significant challenges in thoracic wall reconstruction, whilst reconstruction options vary and are tailored to each patient's needs.Methods: A 66-year-old female diagnosed with phyllodes tumor extending to the 4th and 5th rib undergoes wide excision and partial resection of the 4th and 5th shaft costae, leaving a defect sizing 10 cm6 cm.Hernia (polypropylene) mesh sizing 1 mm was implanted underlay the remaining costae, fixated with stainless steel wires, to prevent lung herniation.Additional semi-rigid titanium mesh sizing 2 mm was implanted onlay the previous hernia mesh to prevent paradoxical movement.A pedicle-based latissimus dorsi flap was raised to reconstruct the soft tissue defect, closed in a multi-layered manner.Periodic assessments were performed to evaluate respiratory function and monitor for potential complications.Results: Adequate chest expansion was observed by the 9th postoperative day, with no indications of paradoxical movement, dehiscence, infection, or seroma noted up to the 14th postoperative day. Conclusion:This study offers compelling evidence that the combination of dual mesh and the latissimus dorsi flap represents a safe and effective method for reconstructing thoracic defects up to 10 centimeters in diameter.Our ongoing research will further examine similar case cohorts to validate these findings and assess the long-term sustainability of these innovative techniques.

Abstract This paper presents a new approach for modeling problems with local discontinuities. The method relies on the finite volume and extended finite element methods. The proposed approach builds on the foundations of the recently introduced Dual Mesh Control Domain Method (DMCDM), which elegantly connects the finite volume and finite element methods. In DMCDM, a primary mesh is used to discretize the domain, and finite element-type interpolation functions are used to build the approximation of the primary state variables. Additionally, a finite volume mesh, referred to as the dual mesh, is used to define the control domains in which integral statements of the governing equations are formulated. The main idea of the proposed approach is to enhance the approximation space of the primary mesh to account for discontinuities by relying on the extended finite element method (XFEM). This is achieved by employing the intrinsic version of XFEM to construct new shape functions that account for the discontinuities in the domain without introducing additional unknowns. The modified shape functions are derived locally near the discontinuity using the moving least squares (MLS) approach. As a result, special shape functions are obtained near the discontinuities, while standard FE shape functions are used elsewhere. While the proposed approach is general, in this study, it is developed for the Poisson equation to demonstrate its performance in the presence of weak discontinuities in the domain. The study shows that the proposed method improves the accuracy and convergence of the finite volume method (FVM) for problems with a local discontinuity in the case of non-conforming meshes.

Point clouds from laser scanners have been widely used in recent research on indoor modeling methods. Currently, particularly in data-driven modeling methods, data preprocessing for dividing structural components and nonstructural components is required before modeling. In this paper, we propose an indoor modeling method without the classification of structural and nonstructural components. A pre-mesh is generated for constructing the adjacency relations of point clouds, and plane components are extracted using planar-based region growing. Then, the distance fields of each plane are calculated, and voxel data referred to as a surface confidence map are obtained. Subsequently, the inside and outside of the indoor model are classified using a graph-cut algorithm. Finally, indoor models with watertight meshes are generated via dual contouring and mesh refinement. The experimental results showed that the point-to-mesh error ranged from approximately 2 mm to 50 mm depending on the dataset. Furthermore, completeness-measured as the proportion of original point-cloud data successfully reconstructed into the mesh-approached 1.0 for single-room datasets and reached around 0.95 for certain multiroom and synthetic datasets. These results demonstrate the effectiveness of the proposed method in automatically removing non-structural components and generating clean structural meshes.

Abstract We introduce a novel property of bounded Voronoi tessellations that enables cycle-free mesh sweeping algorithms. We prove that a topological sort of the dual graph of any Voronoi tessellation is feasible in any flow direction and dimension, allowing straightforward application to discontinuous Galerkin (DG) discretisations of first-order hyperbolic partial differential equations and the Boltzmann Transport Equation (BTE) without requiring flux-cycle corrections. We also present an efficient algorithm to perform the topological sort on the dual mesh nodes, ensuring a valid sweep ordering. This result expands the applicability of DG methods for transport problems on polytopal meshes by providing a robust framework for scalable, parallelised solutions. To illustrate its effectiveness, we conduct a series of computational experiments showcasing a DG scheme for BTE, demonstrating both computational efficiency and adaptability to complex geometries.

Abstract Introduction: Bochdalek hernias are the most common form of congenital diaphragmatic hernia (CDH). While the majority of posterolateral diaphragmatic defects are identified in pediatric patients with respiratory distress, adult patients may remain asymptomatic until later in life. Symptomatic cases in adults are rare and may present with vague respiratory and/or gastrointestinal symptoms. These large hernias may contain multiple intra-abdominal organs at risk for volvulus and strangulation, necessitating timely surgical repair. We present the case of a 73 year-old who underwent successful laparoscopic transabdominal repair of a massive, incarcerated Bochdalek hernia with patch placement. Case Presentation: The patient, a 73 year old male with an active lifestyle as a weightlifter and golfer, initially presented to his primary care physician with a 50-pound unintentional weight loss, poor appetite, dyspnea and fatigue. Computed tomography scan demonstrated a large left sided posterolateral diaphragmatic hernia containing the spleen, pancreatic tail, splenic flexure of the colon, small intestine and a large portion of stomach with mesoaxial volvulus (Fig 1A). After nasogastric decompression of the stomach, he was taken for urgent laparoscopic diaphragmatic hernia repair. Intraoperatively the transverse colon was adherent to the pleura, necessitating division of the gastrohepatic ligament and division of colonic attachments up to the splenic flexure. Once mobilized, the hernia contents were successfully reduced without injury to the spleen. The diaphragmatic defect measured 10 x 15 centimeters and was repaired using Gore Dual Mesh, which was secured to the diaphragm (Fig 1B). On postoperative day one, he tolerated clear liquids after a normal esophagram without leak or obstruction. He then tolerated full liquids on postoperative day two and was discharged to home. Conclusions: Traditionally, open repair of CDH was preferable in younger patients given lower recurrence rates when compared to minimally invasive (MIS) approaches. These repairs can be approached either through a transabdominal or transthoracic approach. MIS transabdominal repair with or without patch placement has more recently gained favor over open repair with comparable recurrence rates. Previous data may have been biased by patient complexity, surgeon preference and technical limitations. Overall, reduction and repair of massive diaphragmatic hernia defects can be achieved via a transabdominal MIS approach with durable results in select patients. Fig 1A. CT depicting large left sided diaphragmatic hernia containing stomach, small intestine, transverse colon, spleen and distal pancreas. 1B. Intraoperative photo of hernia defect with entire spleen in thoracic cavity. 1C. Dual Gore Mesh repair of hernia defect.

Abstract Background Lung herniations are defined as protrusions of pleura covered lung beyond normal anatomic boundaries usually secondary to an abnormal opening. First identified in 1499 and eventually classified in 1845 by anatomy and etiology, lung herniations are relatively rare with fewer than 500 case reports published. Traumatic or post-surgical lung herniations are the more common subcategorizations and usually a secondary differential where physical manipulation/trauma gives rise to the primary condition such as a rib fracture. The following case, however, details a rare presentation of a spontaneous lung herniation (SLIH) from a mild viral upper respiratory infection complicated by an unrelenting cough. Case We report a case of a middle-aged male who required surgical intervention for an anterolateral left lung herniation between the 7th and 8th ribs evidenced coincidentally by CT Angiogram of the chest. His initial symptoms were mild with an agitating cough, pleuritic pain rated about a 4/10 with no radiation, and mild, intermittent shortness of breath. With continued symptoms that had progressed even further into continuous dyspnea, pleuritic pain with inspiration (rated a 8/10 at worst), and a persistent dry cough, he was reassessed with a CT. After discovery of the herniation, the patient was admitted to the operating hospital and a fiberoptic bronchoscopy, cryoablation of ribs 5 to 8, as well as a left sided thoracotomy with direct repair of the chest wall hernia between the 7th and 8th ribs using dual mesh Gore-Tex prosthesis was performed. The patient was cleared by post-op Day 4, and noted complete resolution of all symptoms at 2 week follow up. Discussion SLIH (∼19.8% of all reported lung herniations) is a rare condition marked with variable presentations (most commonly chronic cough and dyspnea) that can present in any patient population but is closely linked to obese and chronic obstructive pulmonary disease patients. CT Thorax is the gold standard diagnostic imaging of choice and is usually completed indirectly with a CT Angiogram due to the high overlap of symptom presentation of pulmonary embolisms. Despite the increased risk of acute surgical intervention, it seems to be the defined first choice over conservative measures for lung herniation repair and our recommendation given the significant benefit with overall symptoms in multiple cases including that of our patient's. Given the potential complications of lung herniation such as lung incarceration, pneumothorax, strangulation (especially with smaller hernias) and pneumomediastinum, cardiothoracic surgery should always be involved for recommendations.

The dual mesh control domain method (DMCDM) is applied, in conjunction with the reduced integration penalty formulation, to solve transient isochoric flow problems of Newtonian fluids, particularly at high Reynolds numbers. The DMCDM is a physically more intuitive method in that the global conservation laws are directly used (akin to the finite volume method), as opposed to the finite element method (FEM), where the weighted integral form of the governing equations is satisfied—an approach that bears little or no physical meaning in the context of fluid flow. However, the DMCDM exploits ideas from the FEM related to interpolation, duality, assembly, and numerical quadrature, allowing for the robust and efficient implementation of the former. In this paper, an element-based, parallelizable formulation for unsteady isochoric flows is investigated, in which the Navier–Stokes equations are semi-discretized using the DMCDM, achieving pressure–velocity coupling through the quadratic penalty method. Unexplored previously in the DMCDM literature, time-dependent problems are addressed, with the time dependence resolved using the alpha-family of approximations to arrive at a fully discretized system of nonlinear algebraic equations. This paper provides insights into implementation aspects, including numerical quadrature and the linearization of the system of equations using Newton's method—both of which have not been presented in detail previously. The ability of the method to capture fine-scale flow features, such as the formation of sub-eddies, is assessed using the lid-driven cavity problem at a high Reynolds number of 10 000. Additionally, the outflow boundary condition is examined using the flow over a backward-facing step problem, and finally, the method's ability to resolve instabilities is tested using the flow past a cylinder problem.

Transplant patients face a risk of developing incisional hernias. Establishing a reliable and secure incisional hernia repair method for this patient population remains a challenge. In this retrospective cohort study, we gathered data from patients who had undergone liver and kidney transplantations and subsequently had developed postoperative incisional hernias. Patient follow-up was extended for a minimum of 18 months. Primary outcomes focused on recurrence, hematoma, and infection rates, comparing the complication profiles of propylene mesh and Dual Mesh incisional hernia repair methods. 122 transplant patients with incisional hernias were included. The incidence of recurrence and infection after incisional hernia repair surgery was 20.6% and 5.9% for Dual Mesh and 22.2% and 9.9% for polypropylene mesh (P = 0.721 and 1.000). In liver recipients, the Dual Mesh method showed a slightly lower incidence of recurrence (17.9% vs. 23.3%) and infection (3.6% vs. 10.0%) compared to polypropylene mesh (P = 0.782, 0.423). Kidney recipients exhibited insignificant higher recurrence (33.3% vs. 19%) and infection rates (16.7% vs. 9.5%) with Dual Mesh (P = 0.588, 0.545). The results suggest that while trends indicate a lower recurrence and infection rate with Dual Mesh in liver transplant patients and a slightly higher recurrence and infection rate with Dual Mesh in kidney transplant patients, these differences were not statistically significant. Therefore, no definitive advantage of one mesh type over the other can be concluded from the data.

A comparative study between condensed polytetrafluoroethylene hernia mesh versus other composite meshes in Endo-laparoscopic ventral hernia repair