Abstract

An unstructured finite element solver to evaluate the ship‐wave problem is presented. The scheme uses a non‐structured finite element algorithm for the Euler or Navier–Stokes flow as for the free‐surface boundary problem. The incompressible flow equations are solved via a fractional step method whereas the non‐linear free‐surface equation is solved via a reference surface which allows fixed and moving meshes. A new non‐structured stabilized approximation is used to eliminate spurious numerical oscillations of the free surface.

Abstract

In the generation of quadrilateral unstructured meshes, special attention is focussed to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the newly generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results in a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases.

Abstract

Abstract

Exascale HPC systems are just about to become available. Such enormous simulation capabilities from the hardware perspective, however, require software that can effectively make efficient use of this massively parallel hardware. For the domain-decomposition based algorithms generally used for CFD, it has become apparent that running one MPI process, i.e. one domain, per CPU core is no longer apt when there are hundreds of cores available per cluster node. There are just too many processes per node that need to communicate with other remote processes. Message aggregation is thus a key aspect of highly scalable parallel codes. A 2-level parallelization featuring a shared-memory level in addition to the MPI process level seems a promising solution. The CODA (CFD for ONERA, DLR, Airbus) software for high-fidelity compressible-flow simulations of industrial configurations implements such a 2-level domaindecomposition hybrid-parallel approach. The processing of unstructured meshes is particularly challenging with respect to load balancing and non-linear data access. For maximum parallel scalability, CODA's parallelization not only features overlapping communication with computation on the process level, but also a dedicated Single Program (on) Multiple Data (SPMD) programming model for the shared-memory level. Here, the design principles of this parallelization concept are outlined, followed by details concerning its implementation in the Flucs infrastructure (FLIS), which has become part of CODA. Moreover, results of scalability studies with CODA are presented, which impressively demonstrate the extreme scalability realized with this parallelization approach. The studies were performed on two distinct HPC clusters, one based on Intel's Xeon Scalable Processor, the other one based on AMD's EPYC.

Abstract

In the generation of quadrilateral unstructured meshes, special attention is focused to the shape of the elements. This is because it is well known that the distortion of the elements and the accuracy of the analysis are closely related. However, in adaptive schemes it is also essential that the new generated mesh meets the prescribed element sizes in order to obtain a solution with the desired precision. In 1982 Giuliani developed a robust rezoning algorithm based on geometrical criteria. It gives proven results is a smooth element size distribution, but elements do not verify the prescribed element size when sharp distributions appear. This paper presents a modification of the Giuliani method that generates non-distorted elements while preserving the element size. Similar to the original method, this modification can be extended to three-dimensional cases

Abstract

Abstract

An unstructured conservative level-set method for two-phase flow with variable surface tension is introduced. Surface tension is a function of temperature or surfactant concentration on the interface. Consequently, the called Marangoni stresses induced by temperature gradients or surfactant concentration gradients on the interface lead to a coupling of momentum transport equation with thermal energy transport equation or interface surfactant transport equation. The finite-volume method discretizes transport equations on 3D collocated unstructured meshes. The unstructured conservative level-set method is employed for interface capturing, whereas the multiple marker approach avoids the numerical coalescence of fluid particles. The fractional-step projection method solves the pressure-velocity coupling. Unstructured flux-limiters are proposed to discretize the convective term of transport equations. A central difference scheme discretizes diffusive terms. Gradients are evaluated by the weighted least-squares method. Verifications and validations are reported.

Abstract

In finite volume schemes with MUSCL interpolation of scalar variables at the faces of control volumes, a slope limiting function is used in order to prevent non-physical oscillations of the solution. More particularly, these functions are designed to ensure a certain monotonicity criterion at each face of the control volume, criterion which then ensures a stability property of the scheme. For vectorial variables, these slope limiting functions are generally applied componentwise, but this may result in a frame-dependance, as well as a loss of accuracy due to false detection of extrema. In this paper, a new vectorial interpolation method is introduced, which is frame-invariant, second-order accurate and stable in a sense that will be defined.