A modified discrete scheme in the Ausas cavitation algorithm

In order to reduce the dependence of accuracy on the number of grids in the Ausas cavitation algorithm, a modified Ausas algorithm was presented. By modifying the mass-conservative Reynolds equation with the concept of linear complementarity problems (LCPs), the coupling of film thickness h and density ratio θ disappeared. The modified equation achieved a new discrete scheme that ensured a complete second-order-accurate central difference scheme for the full film region, avoiding a hybrid-order-accurate discrete scheme. A journal bearing case was studied to show the degree of accuracy improvement and the calculation time compared to a standard LCP solver. The results showed that the modified Ausas algorithm made the asymptotic and convergent behavior with the increase of nodes disappear and allowed for the use of coarse meshes to obtain sufficient accuracy. The calculation time of the modified Ausas algorithm is shorter than the LCP solver (Lemke's pivoting algorithm) for middle and large scale problems.

Combining H-Adaptivity with the Element Splitting Method for Crack Simulation in Large Structures

H-adaptivity is an effective tool to introduce local mesh refinement in the FEM-based numerical simulation of crack propagation. The implementation of h-adaptivity could benefit the numerical simulation of fatigue or accidental load scenarios involving large structures, such as ship hulls. Meanwhile, in engineering applications, the element deletion method is frequently used to represent cracks. However, the element deletion method has some drawbacks, such as strong mesh dependency and loss of mass or energy. In order to mitigate this problem, the element splitting method could be applied. In this study, a numerical method called ‘h-adaptive element splitting’ (h-AES) is introduced. The h-AES method is applied in FEM programs by combining h-adaptivity with the element splitting method. Two examples using the h-AES method to simulate cracks in large structures under linear-elastic fracture mechanics scenario are presented. The numerical results are verified against analytical solutions. Based on the examples, the h-AES method is proven to be able to introduce mesh refinement in large-scale numerical models that mostly consist of structured coarse meshes, which is also beneficial to the reduction of computational resources. By employing the h-AES method, very small cracks are well represented in large structures without any deletions of elements.

Bridging the Multiscale Hybrid-Mixed and Multiscale Hybrid High-Order methods

We establish the equivalence between the Multiscale Hybrid-Mixed (MHM) and the Multiscale Hybrid High-Order (MsHHO) methods for a variable diffusion problem with piecewise polynomial source term. Under the idealized assumption that the local problems defining the multiscale basis functions are exactly solved, we prove that the equivalence holds for general polytopal (coarse) meshes and arbitrary approximation orders. We also leverage the interchange of properties to perform a unified convergence analysis, as well as to improve on both methods.

Sharp Interface Capturing in Compressible Multi-Material Flows with a Diffuse Interface Method

Compressible multi-materialflows are encountered in a wide range of natural phenomena and industrial applications, such as supernova explosions in space, high speed flows in jet and rocket propulsion, underwater explosions, and vapor explosions in post accidental situations in nuclear reactors. In the numerical simulations of these flows, interfaces play a crucial role. A poor numerical resolution of the interfaces could make it difficult to account for the physics, such as material separation, location of the shocks and contact discontinuities, and transfer of the mass, momentum and heat between different materials/phases. Owing to such importance, sharp interface capturing remains an active area of research in the field of computational physics. To address this problem in this paper we focus on the Interface Capturing (IC) strategy, and thus we make use of a newly developed Diffuse Interface Method (DIM) called Multidimensional Limiting Process-Upper Bound (MLP-UB). Our analysis shows that this method is easy to implement, can deal with any number of material interfaces, and produces sharp, shape-preserving interfaces, along with their accurate interaction with the shocks. Numerical experiments show good results even with the use of coarse meshes.

An Arbitrary High Order Well-Balanced ADER-DG Numerical Scheme for the Multilayer Shallow-Water Model with Variable Density

In this work, we present a novel numerical discretization of a variable pressure multilayer shallow water model. The model can be written as a hyperbolic PDE system and allows the simulation of density driven gravity currents in a shallow water framework. The proposed discretization consists in an unlimited arbitrary high order accurate (ADER) Discontinuous Galerkin (DG) method, which is then limited with the MOOD paradigm using an a posteriori subcell finite volume limiter. The resulting numerical scheme is arbitrary high order accurate in space and time for smooth solutions and does not destroy the natural subcell resolution inherent in the DG methods in the presence of strong gradients or discontinuities. A numerical strategy to preserve non-trivial stationary solutions is also discussed. The final method is very accurate in smooth regions even using coarse or very coarse meshes, as shown in the numerical simulations presented here. Finally, a comparison with a laboratory test, where empirical data are available, is also performed.

STUDY OF FROUDE AND HUGHES METHODS BY NUMERICAL TOWING TANK

The resistance of a cargo ship is calculated by numerical towing tank. RANSE multi-phase parallel solver with K-Z SSTturbulent model and VOF formulation is applied. Computational results from double model (without free surface) areused to obtain 1+k in Hughes’ method and those with free surface are analyzed by both Froude and Hughes’ approachesto investigate model and full scale correlation. ITTC recommended uncertainty study is carried out to evaluate numericalerror due to grid density. The computed wave elevation, wake distribution and resistance components by fine, mediumand coarse meshes are cross-compared and validated against experiment data where applicable. It is found that gridresolution has most effect on wave pattern. The predicted friction and viscous-pressure resistance coefficients arerelatively grid independent from present numerical simulation.

Reducing the Dimensionality of Grid Approximations

Предложен общий подход к развитию методов математического моделирования сложных систем. Центральной проблемой, связанной с использованием вычислительной техники, являются сеточные аппроксимации большой размерности и суперЭВМ высокой производительности с большим числом параллельно работающих микропроцессоров. В качестве возможных альтернатив сеточным аппроксимациям большой размерности разрабатываются кинетические методы решения дифференциальных уравнений и методы «склейки» точных решений на грубых сетках. A general approach to the development of complex systems simulation is proposed. The key computer applications problem is the high-dimensional grid approximations and high-performance supercomputers with a large number of parallel CPUs. Kinetic methods for solving differential equations and methods for ”gluing” exact solutions produced with coarse meshes are developed as possible alternatives to high-dimensional grid approximations.  

Combining h-adaptivity with the Element Splitting Method for Crack Simulation in Large Structures

H-adaptivity is an effective tool to introduce local mesh refinement in FEM-based numerical simulation of crack propagation. The implementation of h-adaptivity could benefit the numerical simulation of fatigue or accidental load scenarios involving large structures such as ship hulls. In engineering applications, the element deletion method is frequently used to represent cracks. However, the element deletion method has some drawbacks such as strong mesh dependency and loss of mass or energy. In order to mitigate this problem, the element splitting method could be applied. In this study, a numerical method called ‘h-adaptive element splitting’ (h-AES) is introduced. The h-AES method is applied in FEM programs by combining h-adaptivity with the element splitting method. Two examples using the h-AES method to simulate cracks in large structures under linear-elastic fracture mechanics scenario are presented. The numerical results are verified against analytical solutions. Based on the examples, the h-AES method is proven to be able to introduce mesh refinement in large-scale numerical models that consist of structured coarse meshes. By employing the mesh refinement introduced in this paper, very small cracks are well represented in large structures.

Fine Wrinkling on Coarsely Meshed Thin Shells

We propose a new model and algorithm to capture the high-definition statics of thin shells via coarse meshes. This model predicts global, fine-scale wrinkling at frequencies much higher than the resolution of the coarse mesh; moreover, it is grounded in the geometric analysis of elasticity, and does not require manual guidance, a corpus of training examples, nor tuning of ad hoc parameters. We first approximate the coarse shape of the shell using tension field theory, in which material forces do not resist compression. We then augment this base mesh with wrinkles, parameterized by an amplitude and phase field that we solve for over the base mesh, which together characterize the geometry of the wrinkles. We validate our approach against both physical experiments and numerical simulations, and we show that our algorithm produces wrinkles qualitatively similar to those predicted by traditional shell solvers requiring orders of magnitude more degrees of freedom.