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In this work, transient free surface flows of a viscous incompressible fluid are numerically solved through parallel computation. Transient free surface flows are boundary-value problems of the moving type that involve geometrical nonlinearities. In contrast to more conventional computational fluid dynamics problems, the computational flow domain is partially bounded by a free surface which is not known a priori, since its shape must be computed as part of the solution. In steady flow the free surface is obtained by an iterative process, but when the free surface evolves with time the problem is more difficult as it generates large distortions in the computational flow domain. The incompressible Navier-Stokes numerical solver is based on the finite element method with equal order elements for pressure and velocity (linear elements), and it uses a streamline upwind/Petrov-Galerkin (SUPG) scheme (Hughes, T. J. R., and Brooks, A. N., 1979, 'A Multi-dimensional Upwind Scheme With no Crosswind Diffusion,' in Finite Element Methods for Convection Dominated Flows, ASME ed., 34. AMD, New York, pp. 19-35, and Brooks, A. N., and Hughes, T. J. R., 1982, 'Streamline Upwind/Petrov-Galerkin Formulations for Convection Dominated Flows With Particular Emphasis on the Incompressible Navier-Stokes Equations,' Comput. Methods Appl. Mech. Eng., 32, pp. 199-259) combined with a Pressure-Stabilizing/Petrov-Galerkin (PSPG) one (Tezduyar, T. E., 1992, 'Stablized Finite Element Formulations for Incompressible Flow Computations,' Adv. Appl. Mech., 28, pp. 1-44, and Tezduyar, T. E., Mittal, S., Ray, S. E., and Shih, R., 1992, 'Incompressible Flow Computations With Stabilized Bilinear and Linear Equal Order Interpolation Velocity-Pressure Elements,' Comput. Methods Appl. Mech. Eng., 95, pp. 221-242). At each time step, the fluid equations are solved with constant pressure and null viscous traction conditions at the free surface and the velocities obtained in this way are used for updating the positions of the surface nodes. Then, a pseudo elastic problem is solved in the fluid domain in order to relocate the interior nodes so as to keep mesh distortion controlled. This has been implemented in the PETSc-FEM code (PETSc-FEM: a general purpose, parallel, multi-physics FEM program. GNU general public license (GPL), http://www.cimec.org.ar/petscfem) by running two parallel instances of the code and exchanging information between them. Some numerical examples are presented. [DOI: 10.1115/1.2198246]

Abstract: In this paper we introduce and describe an efficient thread-safe matrix library for computing element/cell residuals and Jacobians in Finite Elements and Finite Volume-like codes. The library provides a wide range of multi-index tensor operations that are normally used in scientific numerical computations. The library implements an algorithm for choosing the optimal computation order when a product of several tensors is performed (i.e., the so-called ‘multi-product’ operation). Another key-point of the FastMat approach is that some computations (for instance the optimal order in the multi-product operation mentioned before) are computed in the first iteration of the loop body and stored in a cache object, so that in the second and subsequent executions these computations are retrieved from the cache, and then not recomputed. The library is open source and freely available within the multi-physics parallel FEM code PETSc-FEM http://www.cimec.org.ar/petscfem and it can be exploited on distributed and shared memory architectures as well as in hybrid approaches. We studied the performance of the library in the context of typical FEM tensor contractions. [Copyright &y& Elsevier]

A semi-analytical computation of the three dimensional Green function for seakeeping low problems is proposed. A potential low model is assumed with an harmonic dependence on time and a linearized free surface boundary condition. The multiplicative Green function is expressed as the product of a time part and a spatial one. The spatial part is known as the Kelvin kernel, which is the sum of two Rankine sources and a wave-like kernel, being the last one written using the Haskind-Havelock representation. Numerical eficiency is improved by an analytical integration of the two Rankine kernels and the use of a singularity subtractive technique for the Haskind-Havelock integral, where a globally adaptive quadrature is performed for the regular part and an analytic integration is used for the singular one. The proposed computation is employed in a low order panel method with lat triangular elements. As a numerical example, an oscillating loating unit hemisphere in heave and surge modes is considered, where analytical and semi-analytical solutions are taken as a reference. [ABSTRACT FROM AUTHOR]

Shock waves and contact discontinuities usually appear in compressible flows, requiring a fine mesh in order to achieve an acceptable accuracy of the numerical solution. The usage of a mesh adaptation strategy is convenient as uniform refinement of the whole mesh becomes prohibitive in three-dimensional (3D) problems. An unsteady h-adaptive strategy for unstructured finite element meshes is introduced. Non-conformity of the refined mesh and a bounded decrease in the geometrical quality of the elements are some features of the refinement algorithm. A 3D extension of the well-known refinement constraint for 2D meshes is used to enforce a smooth size transition among neighbour elements with different levels of refinement. A density-based gradient indicator is used to track discontinuities. The solution procedure is partially parallelised, i.e. the inviscid flow equations are solved in parallel with a finite element SUPG formulation with shock capturing terms while the adaptation of the mesh is sequentially performed. Results are presented for a spherical blast wave driven by a point-like explosion with an initial pressure jump of 105 atmospheres. The adapted solution is compared to that computed on a fixed mesh. Also, the results provided by the theory of self-similar solutions are considered for the analysis. In this particular problem, adapting the mesh to the solution accounts for approximately 4% of the total simulation time and the refinement algorithm scales almost linearly with the size of the problem. [ABSTRACT FROM AUTHOR]

This work encompasses numerical and experimental studies of three-dimensional (3D) sloshing problems. The two-fluid viscous flow, which is solved within a stabilized finite element context, involves liquid and gaseous phases. The free surface is captured with a level set (LS) method, including the bounded renormalization with continuous penalization technique, to avoid the well-known spreading of the marker function. Specifically, this technique is improved with a volume-preserving algorithm for long-term analyses. To verify the numerical model, the responses of free-sloshing cases are compared with analytical solutions and other results computed using a Lagrangian technique. These simulations assess the influence of considering two-dimensional (2D) and 3D analyses, as well as the effects of depth and viscosity. This work presents data obtained from a forced sloshing experiment that is specifically devoted to 3D free surface behaviour. Free surface evolution measurements are used to validate the numerical method. Moreover, the effect of the initial conditions used to promote 3D behaviour in the modelling is evaluated. [ABSTRACT FROM AUTHOR]