Juan M. Gimenez

A fast and accurate method to solve the incompressible Navier‐Stokes equations

Purpose – The purpose of this paper is to highlight the possibilities of a novel Lagrangian formulation in dealing with the solution of the incompressible Navier‐Stokes equations with very large time steps.Design/methodology/approach – The design of the paper is based on introducing the origin of this novel numerical method, originally inspired on the Particle Finite Element Method (PFEM), summarizing the previously published theory in its moving mesh version. Afterwards its extension to fixed mesh version is introduced, showing some details about the implementation.Findings – The authors have found that even though this method was originally designed to deal with heterogeneous or free‐surface flows, it can be competitive with Eulerian alternatives, even in their range of optimal application in terms of accuracy, with an interesting robustness allowing to use large time steps in a stable way.Originality/value – With this objective in mind, the authors have chosen a number of benchmark examples and have pr...

An extended validation of the last generation of particle finite element method for free surface flows

In this paper, a new generation of the particle method known as Particle Finite Element Method (PFEM), which combines convective particle movement and a fixed mesh resolution, is applied to free surface flows. This interesting variant, previously described in the literature as PFEM-2, is able to use larger time steps when compared to other similar numerical tools which implies shorter computational times while maintaining the accuracy of the computation. PFEM-2 has already been extended to free surface problems, being the main topic of this paper a deep validation of this methodology for a wider range of flows. To accomplish this task, different improved versions of discontinuous and continuous enriched basis functions for the pressure field have been developed to capture the free surface dynamics without artificial diffusion or undesired numerical effects when different density ratios are involved. A collection of problems has been carefully selected such that a wide variety of Froude numbers, density ratios and dominant dissipative cases are reported with the intention of presenting a general methodology, not restricted to a particular range of parameters, and capable of using large time-steps. The results of the different free-surface problems solved, which include: Rayleigh-Taylor instability, sloshing problems, viscous standing waves and the dam break problem, are compared to well validated numerical alternatives or experimental measurements obtaining accurate approximations for such complex flows.

gdbOF: A debugging tool for OpenFOAM®

OpenFOAM(R) libraries are a great contribution to CFD community and a powerful way to create solvers and other tools. Nevertheless in this creative process a deep knowledge is needed concerning with classes structure, for value storage in geometric fields and also for matrices resulting from equation systems, becoming a hard task for debugging. To help in this process a new tool, called gdbOF, attachable to gdb (GNU debugger) is presented in this paper. It allows to analyze classes structure at debugging time. This application is implemented by gdb macros, these macros can access to code classes and also to their data in a transparent way, giving the requested information. This tool is tested for different application cases, such as the assemble and storage of matrices in a scalar advective-diffusive problem, non orthogonal correction methods in purely diffusive tests and multiphase solvers based on Volume of Fluid Method. In these tests several types of data are checked, such as: internal and boundary vector and scalar values from solution fields, fluxes in cell faces, boundary patches and boundary conditions. As additional features of this tool data dumping to file and a graphical monitoring of fields are presented. All these capabilities give to gdbOF a wide range of use not only in academic tests but also in real problems.

Conservative handling of arbitrary non-conformal interfaces using an efficient supermesh

This work presents a new and efficient strategy to handle non-conformal interfaces with the aim of assuring the conservation of fluxes in Finite Volume problems. A conservative interpolation is developed for general transport equations. Due to the arbitrary connectivity between the interfaces, the interpolations require flux-based weights defining a complex numerical stencil. In this context, a new method is proposed to simplify the coupling at the interface based on the construction of a simplified supermesh. Here, a supermesh is not completely defined, instead, the interface faces are logically duplicated (or multiplied) to generate a one-to-one connectivity between them. The simplified supermesh named pseudo-supermesh eliminates the interpolations and assures the conservation of fluxes based on the trivial connectivity. The area and the geometrical centroid of the new faces are redefined according to the overlapped sector of the original faces using the local supermeshing approach. Since the arbitrary polygons resulting from the face intersections are not generated and introduced into the mesh, computational cost and implementation efforts are saved. The proposed method is tested focusing on the conservation of fluxes and on the accuracy, showing conservation to machine precision and second order convergence as expected. In order to be able to solve large problems, the methodology is designed and implemented to be run in parallel architectures showing an excellent efficiency.

Numerical Comparison of the Particle Finite Element Method Against an Eulerian Formulation

The main goal of this paper is to validate experimentally the principal conclusions previously published in [17]. Two manufactured test cases were considered with their respective analytic solutions. First, a scalar transport equation is considered written in such a way that several parameters are included to stress the limiting situation where the Eulerian and the Lagrangian approaches behave better. The results show conditions to be fulfilled in order to choose between both formulations, according to the problem parameters. A brief discussion about the projection needed for PFEM-2 method is included, specially due to its impact on the error convergence rate. Lately, an extension to Navier-Stokes equations is introduced using also a manufactured case to verify again the same conclusions. This paper intends to establish the first steps towards a mathematical error analysis for the particle finite element method which supports the preliminary theoretical and experimental results presented here.

Recent Advances in the Particle Finite Element Method Towards More Complex Fluid Flow Applications

This paper presents a state of the art in the Particle Finite Element Method, normally called PFEM, its emphasis in the new ideas oriented to extend its application not only to solve fluid structure interaction and multifluid problems, also bring new opportunities to shorten the gap between engineering design times and computational simulation times for general problems when Eulerian formulation were typically chosen. In order to reduce the long history of this method here the starting point begins with the reformulation of the method to solve academic and real problems in real time or at least in drastically reduced computational times. The main topics involved in this paper are around the stability and the accuracy of Lagrangian formulations against its Eulerian counterpart shown through several academic benchmarks and a deep analysis of the efficiency revealing that the original method needs some new features. The former brought out a new integration method called X-IVAS and the later has produced a new version of the method called PFEM in fixed Mesh. Once the method had shown its good performance and how the new features impact on the final efficiency the last developments had been done in extending the application of this new method in multifluids and other complex fluid mechanics problems like turbulence and reactive flows.