Algebraic Discrete Nonlocal (DNL) Absorbing Boundary Condition for the Ship Wave Resistance Problem

An absorbing boundary condition for the ship wave resistance problem is presented. In contrast to the Dawson-like methods, it avoids the use of numerical viscosities in the discretization, so that a centered scheme can be used for the free surface operator. The absorbing boundary condition is “completely absorbing,” in the sense that the solution is independent of the position of the downstream boundary and is derived from straightforward analysis of the resulting constant-coefficients difference equations, assuming that the mesh is 1D-structured (in the longitudinal direction) and requires the eigen-decomposition of a matrix one dimension lower than the system matrix. The use of a centered scheme for the free surface operator allows a full finite element discretization. The drag is computed by a momentum flux balance. This method is more accurate and guarantees positive resistances

Computing ship wave resistance from wave amplitude with a non‐local absorbing boundary condition

A method for computing ship wave resistance from a momentum flux balance is presented. It is based on computing the momentum flux carried by the gravity waves that exit the computational domain through the outlet plane. It can be shown that this method ensures a non‐negative wave‐resistance, in contrast with straightforward integration of the normal pressure forces. However, this calculation should be performed on a transverse plane located far behind the ship. Traditional Dawson‐like methods add a numerical viscosity that dampens the wave pattern so that some amount of momentum flux is lost, and resulting in an error in the momentum balance. The flow field is computed, then, with a centred scheme with absorbing boundary conditions

Simulation of free-surface flows by a finite element interface capturing technique

Transient free-surface (FS) flows are numerically simulated by a finite element interface capturing method based on a level set approach. The methodology consists of the solution of two-fluid viscous incompressible flows for a single domain, where the liquid phase is identified by the positive values of the level set function, the gaseous phase by negative ones, and the FS by the zero level set. The numerical solution at each time step is performed in three stages: (i) a two-fluid Navier-Stokes stage, (ii) an advection stage for the transport of the level set function and (iii) a bounded reinitialisation with continuous penalisation stage for keeping smoothness of the level set function. The proposed procedure, and particularly the renormalisation stage, is evaluated in three typical two- and threedimensional problems.Fil: Battaglia, Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Hierarchical boundary element method based on the Barnes-Hut tree applied to exterior creeping flow

En este trabajo se exponen un método de elementos de borde en una variante jerárquica y su empleo en flujo de Stokes alrededor de cuerpos rígidos tridimensionales en régimen estacionario. La propuesta se basa en el algoritmo jerárquico de bajo orden descendente y autoadaptativo de Barnes-Hut, que se emplea junto con una formulación integral de contorno indirecta y de segunda clase cuyo término fuente es función de la velocidad no perturbada. El campo solución es la densidad superficial de capa doble modificada para completar el espectro de autovalores del operador integral. De esta manera, los modos rígidos son eliminados y se pueden representar una fuerza y una cupla no nulas sobre el cuerpo. Los elementos son triángulos planos de bajo orden y se emplea una resolución iterativa mediante residuo mínimo generalizado (GMRES) sin precondicionamiento. Los ejemplos numéricos incluyen casos con soluciones analíticas, cuerpos con aristas y vértices o con formas intrincadas. La ventaja principal de la técnica desarrollada se halla en la posibilidad de considerar un número de grados de libertad mayor respecto a los que pueden emplearse con los métodos de colocación al centroide más tradicionales, debido a la disminución de la demanda de memoria primaria y de los tiempos de cómputo.In this work, a hierarchical variant of a boundary element method and its use in Stokes flow around three-dimensional rigid bodies in steady regime is presented. The proposal is based on the descending hierarchical low-order and self-adaptive algorithm of Barnes-Hut, and it is used in conjunction with an indirect boundary integral formulation of second class, whose source term is a function of the undisturbed velocity. The solution field is the double layer surface density, which is modified in order to complete the eigenvalue spectrum of the integral operator. In this way, the rigid modes are eliminated and both a non-zero force and a non-null torque on the body could be calculated. The elements are low order flat triangles, and an iterative solution by generalized minimal residual (GMRES) is used. Numerical examples include cases with analytical solutions, bodies with edges and vertices, or with intricate shapes. The main advantage of the presented technique is the possibility of considering a greater number of degrees of freedom regarding traditional collocation methods, due to the decreased demand of main memory and the reduction in the computation times.Fil: Sarraf, Sofia Soledad. Universidad Nacional del Comahue. Facultad de Ingeniería. Departamento de Mecánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Battaglia, Laura. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina. Universidad Tecnologica Nacional; ArgentinaFil: Lopez, Ezequiel Jose. Universidad Nacional del Comahue. Facultad de Ingeniería. Departamento de Mecánica; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

Numerical simulation of the flow around the ahmed vehicle model

The unsteady flow around the Ahmed vehicle model is numerically solved for a Reynolds number of 4.25 million based on the model length. A viscous and incompressible fluid flow of Newtonian type governed by the Navier-Stokes equations is assumed. A Large Eddy Simulation (LES) technique is applied together with the Smagorinsky model as Subgrid Scale Modeling (SGM) and a slightly modified van Driest near-wall damping. A monolithic computational code based on the finite element method is used, with linear basis functions for both pressure and velocity fields, stabilized by means of the Streamline Upwind Petrov-Galerkin (SUPG) scheme combined with the Pressure Stabilizing Petrov- Galerkin (PSPG) one. Parallel computing on a Beowulf cluster with a domain decomposition technique for solving the algebraic system is used. The flow analysis is focused on the near-wake region, where the coherent macro structures are estimated through the second invariant of the velocity gradient (or Q-criterion) applied on the time-average flow. It is verified that the topological features of the timeaverage flow are independent of the averaging time T and grid-size.Fil: Franck, Gerardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentina. Universidad Tecnologica Nacional; ArgentinaFil: Nigro, Norberto Marcelo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; ArgentinaFil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Instituto de Desarrollo Tecnológico para la Industria Química. Universidad Nacional del Litoral. Instituto de Desarrollo Tecnológico para la Industria Química; Argentin

Coupling Concept of two Parallel Research Codesfor Two and Three Dimensional Fluid Structure Interaction Analysis

This paper discuss a coupling strategy of two different software packages to provide fluid structure interaction (FSI) analysis. The basic idea is to combine the advantages of the two codes to create a powerful FSI solver for two and three dimensional analysis. The fluid part is computed by a program called PETSc-FEM a software developed at Centro de Investigacion de Metodos Computacionales CIMEC. The structural part of the coupled process is computed by the research code elementary Parallel Solver (ELPASO) of the Technische Universitat Braunschweig, Institut fur Konstruktionstechnik (IK).Fil: Garelli, Luciano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Schauer, Marco. Technische Universität Braunschweig; AlemaniaFil: D'elia, Jorge. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Storti, Mario Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Santa Fe. Centro de Investigaciones En Metodos Computacionales. Universidad Nacional del Litoral. Centro de Investigaciones En Metodos Computacionales; ArgentinaFil: Langer, Sabine C.. Technische Universität Braunschweig; Alemani

The DNL absorbing boundary condition: applications to wave problems

A general methodology for developing absorbing boundary conditions is presented. For planar surfaces, it is based on a straightforward solution of the system of block difference equations that arise from partial discretization in the directions transversal to the artificial boundary followed by discretization on a constant step 1D grid in the direction normal to the boundary. This leads to an eigenvalue problem of the size of the number of degrees of freedom in the lateral discretization. The eigenvalues are classified as right- or left-going and the absorbing boundary condition consists in imposing a null value for the ingoing modes, leaving free the outgoing ones. Whereas the classification is straightforward for operators with definite sign, like the Laplace operator, a virtual dissipative mechanism has to be added in the mixed case, usually associated with wave propagation phenomena, like the Helmholtz equation. The main advantage of the method is that it can be implemented as a black-box routine, taking as input the coefficients of the linear system, obtained from standard discretization (FEM or FDM) packages and giving on output the absorption matrix. We present the application of the DNL methodology to typical wave problems, like Helmholtz equations and potential flow with free surface (the ship wave resistance and sea-keeping problems)

The DNL absorbing boundary condition: applications to wave problems

A general methodology for developing absorbing boundary conditions is presented. For planar surfaces, it is based on a straightforward solution of the system of block difference equations that arise from partial discretization in the directions transversal to the artificial boundary followed by discretization on a constant step 1D grid in the direction normal to the boundary. This leads to an eigenvalue problem of the size of the number of degrees of freedom in the lateral discretization. The eigenvalues are classified as right- or left-going and the absorbing boundary condition consists in imposing a null value for the ingoing modes, leaving free the outgoing ones. Whereas the classification is straightforward for operators with definite sign, like the Laplace operator, a virtual dissipative mechanism has to be added in the mixed case, usually associated with wave propagation phenomena, like the Helmholtz equation. The main advantage of the method is that it can be implemented as a black-box routine, taking as input the coefficients of the linear system, obtained from standard discretization (FEM or FDM) packages and giving on output the absorption matrix. We present the application of the DNL methodology to typical wave problems, like Helmholtz equations and potential flow with free surface (the ship wave resistance and sea-keeping problems)

The Twisted Gradient Flow strong coupling with Parallel Tempering on Boundary Conditions

We present a proposal for calculating the running of the coupling constant of the $\mathrm{SU}(3)$ pure-gauge theory, which combines the Twisted Gradient Flow (TGF) renormalization scheme with Parallel Tempering on Boundary Conditions (PTBC). The TGF is a gradient flow-based renormalization scheme formulated in an asymmetric lattice with twisted boundary conditions. Combined with step scaling, it has been successfully used to calculate the $\mathrm{SU}(3)$ $\Lambda$ parameter. As with all gradient flow-based schemes, the coupling constant is highly correlated with the topological charge and affected by topology freezing, an issue addressed by projecting the determination of the coupling onto the zero topological sector. As an alternative to the zero-charge projection, we combine TGF with PTBC, by replicating multiple copies of the same lattice, interpolating between periodic and open boundary conditions in a parallel-tempered manner. We present a first exploration of these ideas by analyzing specific ensembles of $\mathrm{SU}(3)$ lattices with and without PTBC.Comment: 11 pages, 5 figures, 40th International Symposium on Lattice Field Theory, LATTICE2023 Fermilab, Batavia, Illinois, USA, from July 31 to August 4, 2023. V2: text unchanged, some previous figures were not correct and have been update