A new family of semi-implicit Finite Volume / Virtual Element methods for incompressible flows on unstructured meshes

We introduce a new family of high order accurate semi-implicit schemes for the solution of non-linear hyperbolic partial differential equations on unstructured polygonal meshes. The time discretization is based on a splitting between explicit and implicit terms that may arise either from the multi-scale nature of the governing equations, which involve both slow and fast scales, or in the context of projection methods, where the numerical solution is projected onto the physically meaningful solution manifold. We propose to use a high order finite volume (FV) scheme for the explicit terms, ensuring conservation property and robustness across shock waves, while the virtual element method (VEM) is employed to deal with the discretization of the implicit terms, which typically requires an elliptic problem to be solved. The numerical solution is then transferred via suitable L2 projection operators from the FV to the VEM solution space and vice-versa. High order time accuracy is achieved using the semi-implicit IMEX Runge-Kutta schemes, and the novel schemes are proven to be asymptotic preserving and well-balanced. As representative models, we choose the shallow water equations (SWE), thus handling multiple time scales characterized by a different Froude number, and the incompressible Navier-Stokes equations (INS), which are solved at the aid of a projection method to satisfy the solenoidal constraint of the velocity field. Furthermore, an implicit discretization for the viscous terms is devised for the INS model, which is based on the VEM technique. Consequently, the CFL-type stability condition on the maximum admissible time step is based only on the fluid velocity and not on the celerity nor on the viscous eigenvalues. A large suite of test cases demonstrates the accuracy and the capabilities of the new family of schemes to solve relevant benchmarks in the field of incompressible fluids

Second order ADER scheme for advection-diffusion on moving overset grids with a compact transmission condition

We propose a space-time Finite Volume scheme on moving Chimera grids for a general advection-diffusion problem. Special care is devoted to grid overlapping zones in order to devise a compact and accurate discretization stencil to exchange information between different mesh patches. Like in the ADER method, the equations are discretized on a space-time slab. Thus, instead of time-dependent spatial transmission conditions between relatively moving grid blocks, we define interpolation polynomials on arbitrarily intersecting space-time cells at the block boundaries. \rtwo{Through this scheme, a mesh-free FEM-predictor/FVM-corrector approach is employed for representing the solution.} In this discretization framework, a new space-time Local Lax-Friederichs (LLF) stabilization speed is defined by considering both the advective and diffusive nature of the equation. The numerical illustrations for linear and non-linear systems show that background and foreground moving meshes do not introduce spurious perturbation to the solution, uniformly reaching second order accuracy in space and time. Finally, it is shown that several foreground meshes, possibly overlapping and with independent displacements, can be employed thanks to this approach

Second Order ADER Scheme for Unsteady Advection-Diffusion on Moving Overset Grids with a Compact Transmission Condition

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ADER scheme for incompressible Navier-Stokes equations on Overset grids with a compact transmission condition

A space-time Finite Volume method is devised to simulate incompressible viscous flows in an evolving domain. Inspired by the ADER method, the Navier-Stokes equations are discretized onto a space-time overset grid which is able to take into account both the shape of a possibly moving object and the evolution of the domain. A compact transmission condition is employed in order to mutually exchange information from one mesh to the other. The resulting method is second order accurate in space and time for both velocity and pressure. The accuracy and efficiency of the method are tested through reference simulations.Une méthode des volumes finis spatio-temporels est conçue pour simuler des écoulements visqueux incompressibles dans un domaine évolutif. Inspirée de la méthode ADER, les équations de Navier-Stokes sont discrétisées sur un maillage spatio-temporel overset qui est capable de prendre en compte à la fois la forme d’un objet éventuellement en mouvement et l’évolution du domaine. Une condition de transmission compacte est employée afin d’échanger mutuellement des informations d’un maillage à l’autre. La méthode résultante est d’une précision de second ordre dans l’espace et dans le temps pour la vitesse et la pression. La précision et l’efficacité de la méthode sont testées sur des cas test pris de la littérature

Geometry description and mesh construction from medical imaging∗

We present a new method for defining and meshing patient-specific domains from medical images. Our approach is based on an atlas image segmentation technique, and relies on the modular registration algorithm of S. Bertoluzza et al. [25]. The mesh of the patient-specific domain is generated by deforming the corresponding mesh on an a priori segmented and meshed reference image (the atlas). Our method aims at automating the process at the interface of medical imaging and numerical simulation, thus reducing the computational cost in those situations where simulations have to be managed on numerous medical images of similar patients

Search for dark matter produced in association with bottom or top quarks in √s = 13 TeV pp collisions with the ATLAS detector

A search for weakly interacting massive particle dark matter produced in association with bottom or top quarks is presented. Final states containing third-generation quarks and miss- ing transverse momentum are considered. The analysis uses 36.1 fb−1 of proton–proton collision data recorded by the ATLAS experiment at √s = 13 TeV in 2015 and 2016. No significant excess of events above the estimated backgrounds is observed. The results are in- terpreted in the framework of simplified models of spin-0 dark-matter mediators. For colour- neutral spin-0 mediators produced in association with top quarks and decaying into a pair of dark-matter particles, mediator masses below 50 GeV are excluded assuming a dark-matter candidate mass of 1 GeV and unitary couplings. For scalar and pseudoscalar mediators produced in association with bottom quarks, the search sets limits on the production cross- section of 300 times the predicted rate for mediators with masses between 10 and 50 GeV and assuming a dark-matter mass of 1 GeV and unitary coupling. Constraints on colour- charged scalar simplified models are also presented. Assuming a dark-matter particle mass of 35 GeV, mediator particles with mass below 1.1 TeV are excluded for couplings yielding a dark-matter relic density consistent with measurements