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This paper describes the first steps of development of a new multidimensional time implicit code devoted to the study of hydrodynamical processes in stellar interiors. The code solves the hydrodynamical equations in spherical geometry and…
When representing convective instability mechanisms with the streamwise BiGlobal stability approach, results suffer from a sensitivity to the streamwise domain truncation length and boundary conditions. The methodology proposed in this…
This paper investigates the design of a subclass of time-varying Control Barrier Functions (CBFs), specifically that of uniformly time-varying CBFs. Leveraging the fact that CBFs encode a system's dynamic capabilities relative to a state…
The article describes the CFD software tool FlowVision (OOO "Tesis", Moscow). The model equations used for this research are the set of Reynolds and continuity equations and equations of the standard k - e turbulence model. The aim of the…
A framework for exponential time discretization of the multilayer rotating shallow water equations is developed in combination with a mimetic discretization in space. The method is based on a combination of existing exponential time…
This paper presents a new method to approximate the time-dependent convection-diffusion equations using conforming finite element methods, ensuring that the discrete solution respects the physical bounds imposed by the differential…
Computational Fluid Dynamics (CFD) simulation by the numerical solution of the Navier-Stokes equations is an essential tool in a wide range of applications from engineering design to climate modeling. However, the computational cost and…
Local time-stepping methods permit to overcome the severe stability constraint on explicit methods caused by local mesh refinement without sacrificing explicitness. In \cite{DiazGrote09}, a leapfrog based explicit local time-stepping…
The application of immersed boundary methods in static analyses is often impeded by poorly cut elements (small cut elements problem), leading to ill-conditioned linear systems of equations and stability problems. While these concerns may…
We consider a family of conforming space-time finite element discretizations for the wave equation based on splines of maximal regularity in time. Traditional techniques may require a CFL condition to guarantee stability. Recent works by O.…
The present work proposes an inflow turbulence generation strategy using deep learning methods. This is achieved with the help of an autoencoder architecture with two different types of operational layers in the latent-space: a fully…
The objective is to provide clear and well-motivated guidance to Machine Learning (ML) teams, founded on our experience in empirical turbulence modeling. Guidance is also needed for modeling outside ML. ML is not yet successful in…
Control barrier functions (CBFs) have seen widespread success in providing forward invariance and safety guarantees for dynamical control systems. A crucial limitation of discrete-time formulations is that CBFs that are nonconcave in their…
We present a new energy-stable open boundary condition, and an associated numerical algorithm, for simulating incompressible flows with outflow/open boundaries. This open boundary condition ensures the energy stability of the system, even…
The never-ending computational demand from simulations of turbulence makes computational fluid dynamics (CFD) a prime application use case for current and future exascale systems. High-order finite element methods, such as the spectral…
We present the Fully cOUpled loCAl model of sUperfLuid Turbulence (FOUCAULT) that describes the dynamics of finite temperature superfluids. The superfluid component is described by the vortex filament method while the normal fluid is…
We present a high-order radial basis function finite difference (RBF-FD) framework for the solution of advection-diffusion equations on time-varying domains. Our framework is based on a generalization of the recently developed Overlapped…
Set invariance techniques such as control barrier functions (CBFs) can be used to enforce time-varying constraints such as keeping a safe distance from dynamic objects. However, existing methods for enforcing time-varying constraints often…
A computational fluid dynamics (CFD) simulation framework for fluid-flow prediction is developed on the Tensor Processing Unit (TPU) platform. The TPU architecture is featured with accelerated dense matrix multiplication, large high…
We present a novel method for designing higher-order Control Barrier Functions (CBFs) that guarantee convergence to a safe set within a user-specified finite. Traditional Higher Order CBFs (HOCBFs) ensure asymptotic safety but lack…