A fast moving least squares approximation with adaptive Lagrangian mesh refinement for large scale immersed boundary simulations

This paper describes the development of a numerical model of a jack-up leg supported on the seabed and the study performed in order to analyze the interaction at the interface between the soil and its spudcan. Self-elevating units or jack-ups are widely used for offshore operations and the strength of their whole structure is to be ensured for the environmental conditions encountered during the operations. This is why the determination of the soil-spudcan interface is a major challenge since it depends on a wide range of factors, such as sea conditions, properties of the soil, geometry and material of the structure, etc. In light of the unpredictable and non-linear behavior of the marine environment and the soil, it is necessary to develop further studies on this subject to reduce uncertainties and to ensure the safety of offshore structures, as most of the failures in the offshore oil platforms are related to foundations. To do so, different approaches have been used: • Abaqus/ Standard and Abaqus/Explicit solvers; • Rigid bodies and deformable bodies afterwards; • Three kind of meshes: ○ Lagrangian mesh; ○ Arbitrary Lagrangian - Eulerian mesh; ○ Coupled Eulerian - Lagrangian mesh. To validate the model and the results obtained numerically in the end of the project, a comparison with an analytical calculation of the spudcan penetration has to be performed, based on the geometry of the structure and the properties of the soil.

Towards adaptive kinetic-fluid simulations of weakly ionized plasmas

Summary An adaptive three-dimensional mesh refinement method based on the law of mass conservation has been introduced and tested using some analytical velocity fields as accurate in identifying singular point, asymptotic plane and drawing closed streamlines. This paper further investigates the adaptive mesh refinement method using a velocity field that is due to a uniform strain and a point vortex. Similar results have been obtained.

Computational fluid dynamics (CFD) are at the forefront of computational mechanics in requiring large-scale computational resources associated with high performance computing (HPC). Many flows of practical interest also include moving and deforming boundaries. High fidelity computations of fluid-structure interactions (FSI) are amongst the most challenging problems in computational mechanics. Additionally, many FSI applications have different resolution requirements in different parts of the domain and therefore requirement adaptive mesh refinement (AMR) for computational efficiency. FLASH is a well established AMR code with an existing Lagrangian framework which could be augmented and exploited to implement an immersed boundary method for simulating fluid-structure interactions atop an existing infrastructure. This paper describes the augmentations to the Lagrangian framework, and the new parallel algorithms added to the FLASH infrastructure that enabled the implementation of immersed boundary method in FLASH. The paper also presents scaling behavior and performance analysis of the implementations.

The meshless regular hybrid boundary node method for 2D linear elasticity

Although a human eye comprises less than 0.1% of the frontal body surface area, injuries to the eye are found to be disproportionally common in survivors of explosions. This study aimed to introduce a Lagrangian–Eulerian coupling model to predict globe rupture resulting from primary blast effect. A finite element model of a human eye was created using Lagrangian mesh. An explosive and its surrounding air domain were modelled using Eulerian mesh. Coupling the two models allowed simulating the blast wave generation, propagation and interaction with the eye. The results showed that the peak overpressures caused by blast wave on the corneal apex are 2080, 932.1 and 487.3 kPa for the victim distances of 0.75, 1.0 and 1.25 m, respectively. Higher stress occurred at the limbus, where the peaks for the three victim distances are 25.5, 14.1 and 6.4 MPa. The overpressure threshold of globe rupture was determined as 2000 kPa in a small-scale explosion. The findings would provide insights into the mechanism of primary blast-induced ocular injuries.

<p>We present an accurate and fast finite element solver for global electromagnetic induction forward modeling problems in spherical Earth. We solve for the electric field equation using the first-order Nedelec elements. The magnetic field is then obtained by computing the curl of the electric field. The computational domain composed of the air space and the conductive Earth is discretized by disjoint unstructured tetrahedral elements. To improve the accuracy with an optimal number of unknowns, we propose a simple two-step goal-oriented adaptive mesh refinement (AMR) strategy. In the first step, an h-type AMR procedure is used to obtain an optimal finite element mesh. The mesh refinement is accomplished by bisection to generate a set of hierarchal tetrahedral meshes. The AMR procedure is driven by a goal-oriented error estimator, which is based on face jumps of normal components of current density. In the second step, we adopt the high-order finite elements at the last iteration to update the accuracy of final numerical solutions. This simple two-step adaptive strategy takes advantage of both h-type AMR and high-order basis functions, and in the meanwhile, it is also computationally economical. To improve efficiency, the solver is parallelized with an MPI-based domain decomposition technique. The sophisticated auxiliary space preconditioned linear solver is adopted to efficiently solve the linear system of equations. This new solver is verified on both semi-analytic and realistic 3-D Earth models. It can be used as a core to derive the inversion of global electromagnetic induction data.</p><p> </p>

In this paper the two-dimensional Euler equations, with a simple chemical reaction model, are used as the governing equations for the detonation problem. The spatial derivatives are evaluated using the fifth-order WENO scheme, and the third-order TVD Runge-Kutta method is employed for the temporal derivative. The characteristics of the two-dimensional detonation in an argon-diluted mixture of hydrogen and oxygen are investigated using Adaptive Mesh Refinement (AMR) method. From computational accuracy point of view, AMR enables the detonation front to be clearer than the method with basic meshes. From the other point of computational time, AMR also saves about half the time as compared with the case of refining the entire field. It is obvious that AMR not only increases the resolution of local field, but also improves the efficiency of numerical simulation.

On the discretized delta function and force calculation in the immersed boundary method

Robust adaptive mesh refinement for transonic conditions is one of the most difficult challenges to advancing CFD usage for certification by analysis. Transonic fluid-structure interaction cases represent an even more difficult challenge for adaptive mesh refinement. Production aircraft furthermore have structural models that have gaps and discontinuities that make the interdomain transfer of loads and deflections difficult. This adds to the challenge of adaptive mesh refinement. An initial attempt to create an adaptive mesh refinement process that refines regions of high flow gradient based around the HeldenMesh software is presented. The method is applied to the Integrated Adaptive Wing Technology Maturation (IAWTM) configuration. That has developed an aspect ratio 13.5 wing aeroelastic wind-tunnel model for testing in the Transonic Dynamics Tunnel (TDT). The high levels of deformation of this wing make the adaptation of meshes for the static shape difficult and has necessitated some creativity in how to efficiently adapt meshes. A time-domain identification of the unsteady system based on flexible modes using the adapted meshes is performed.

Adaptive Mesh and Algorithm Refinement Using Direct Simulation Monte Carlo

The intensity variation in a scanning electron microscope is a complex function of sample topography and composition. Measurement accuracy is improved when an explicit accounting for the relationship between signal and measurand is made. Because the determinants of the signal are many, the theoretical understanding usually takes the form of a simulator. For samples with nonconducting regions that charge, one phase of the simulation is finite element analysis to compute the electric field. The size of the finite element mesh, and consequently computation time, can be reduced through the use of adaptive mesh refinement. We present a new a posteriori local error estimator and adaptive mesh refinement algorithm for the scanning electron microscope simulation. This error estimate is designed to minimize the error in the electron trajectories, rather than the energy norm of the error that traditional error estimators minimize. Using a test problem with a known exact solution, we show that the adaptive mesh can achieve the same error in electron trajectories as a carefully designed hand-graded mesh while using 3.5 times fewer vertices and 2.25 times less computation time.

Abstract. This study describes the numerical implementation, verification and validation of an immersed boundary method (IBM) in the atmospheric solver Meso-NH for applications to urban flow modeling. The IBM represents the fluid–solid interface by means of a level-set function and models the obstacles as part of the resolved scales. The IBM is implemented by means of a three-step procedure: first, an explicit-in-time forcing is developed based on a novel ghost-cell technique that uses multiple image points instead of the classical single mirror point. The second step consists of an implicit step projection whereby the right-hand side of the Poisson equation is modified by means of a cut-cell technique to satisfy the incompressibility constraint. The condition of non-permeability is achieved at the embedded fluid–solid interface by an iterative procedure applied on the modified Poisson equation. In the final step, the turbulent fluxes and the wall model used for large-eddy simulations (LESs) are corrected, and a wall model is proposed to ensure consistency of the subgrid scales with the IBM treatment. In the second of part of the paper, the IBM is verified and validated for several analytical and benchmark test cases of flows around single bluff bodies with an increasing level of complexity. The analysis showed that the Meso-NH model (MNH) with IBM reproduces the expected physical features of the flow, which are also found in the atmosphere at much larger scales. Finally, the IBM is validated in the LES mode against the Mock Urban Setting Test (MUST) field experiment, which is characterized by strong roughness caused by the presence of a set of obstacles placed in the atmospheric boundary layer in nearly neutral stability conditions. The Meso-NH IBM–LES reproduces with reasonable accuracy both the mean flow and turbulent fluctuations observed in this idealized urban environment.

In this work, a virtual body-fitted grid is introduced and combined with the implicit velocity correction-based immersed boundary method (IBM) for simulation of incompressible flows with moving boundaries. The original implicit velocity correction-based IBM to this kind of problem requires the matrix inversion operation to be repeated at each time step, resulting in significant computational resources and time when the Gaussian elimination method is used for solution, whose computational complexity is $\mathcal{O}(M^3).$ The present method introduces a virtual body-fitted grid that moves together with the immersed boundary to overcome the above defect. As with the original implicit velocity correction-based IBM, the fractional step technique, which includes the prediction step and the correction step, is applied in the present method. Note that the correction step is implemented on the virtual grid in the present method instead of the Eulerian mesh in the original method. Since the relative positions between virtual grid points and Lagrangian points are changeless, the matrix in the correction step can be pre-calculated and stored, avoiding the need to update it at every time step. Although, within this approach, three additional steps including the marking virtual grid points and covered Eulerian points, and two interpolations between the Eulerian mesh and the virtual grid must be conducted at each time step, the computational effort is still greatly reduced as the computational complexity of these steps is $\mathcal{O}(M).$ A numerical experiment of flow around a transversely oscillating cylinder is first performed, demonstrating the improved efficiency, especially when the number of Lagrangian points is large. As validation, the flow over a flapping elliptical wing and a fluid-structure interaction (FSI) problem of vortex-induced vibrations of a circular cylinder are simulated. The numerical results are found to be in line with reference results, verifying the ability of the proposed method to simulate complex moving boundary problems.

An explicit finite element based solution procedure for solving the equations of compressible viscous high speed flow is presented. The method uses domain splitting to advance the solution with different timesteps on different portions of the mesh. For steady inviscid flows, adaptive mesh refinement procedures are successfully employed to enhance the definition of discontinuities. Preliminary ideas on the application of adaptive mesh refinement to the solution of problems involving steady viscous flow are presented. Sample timings are given for the performance of the finite element code on modern supercomputers.