Related papers: A low-rank algorithm for weakly compressible flow
Particle-based stochastic approximations of the Boltzmann equation are popular tools for simulations of non-equilibrium gas flows, for which the Navier-Stokes-Fourier equations fail to provide accurate description. However, these numerical…
Fluid flows are omnipresent in nature and engineering disciplines. The reliable computation of fluids has been a long-lasting challenge due to nonlinear interactions over multiple spatio-temporal scales. The compressible Navier-Stokes…
The construction of weak solutions to compressible Navier-Stokes equations via a numerical method (including a rigorous proof of the convergence) is in a short supply, and so far, available only for one sole numerical scheme suggested in…
In this paper, we propose a method for the approximation of the solution of high-dimensional weakly coercive problems formulated in tensor spaces using low-rank approximation formats. The method can be seen as a perturbation of a minimal…
Modelling rarefied gas flow via the Boltzmann equation plays a vital role in many areas. Due to the high dimensionality of this kinetic equation and the coexistence of multiple characteristic scales in the transport processes, conventional…
Slow flows of a slightly rarefied gas under high thermal stresses are considered. The correct fluid-dynamic description of this class of flows is based on the Kogan--Galkin--Friedlander equations, containing some non-Navier--Stokes terms in…
We present a component-based model order reduction procedure to efficiently and accurately solve parameterized incompressible flows governed by the Navier-Stokes equations. Our approach leverages a non-overlapping optimization-based domain…
A fully discrete Crank--Nicolson Leap--Frog (CNLF) scheme is proposed and analyzed for the unsteady bioconvection flow problem with concentration-dependent viscosity. Spatial discretization is handled via the Galerkin finite element method…
The dynamical low-rank approximation of time-dependent matrices is a low-rank factorization updating technique. It leads to differential equations for factors of the matrices, which need to be solved numerically. We propose and analyze a…
We present a hybrid lattice Boltzmann algorithm for the simulation of flow glass-forming fluids, characterized by slow structural relaxation, at the level of the Navier-Stokes equation. The fluid is described in terms of a nonlinear…
We consider dynamical low-rank approximation (DLRA) for the numerical simulation of Vlasov--Poisson equations based on separation of space and velocity variables, as proposed in several recent works. The standard approach for the time…
In this paper, we propose a general framework to design asymptotic preserving schemes for the Boltzmann kinetic kinetic and related equations. Numerically solving these equations are challenging due to the nonlinear stiff collision (source)…
Convection is an important physical process in astrophysics well-studied using numerical simulations under the Boussinesq and/or anelastic approximations. However these approaches reach their limits when compressible effects are important…
A new algorithm for solving the Navier-Stokes equations (NSE) on a quantum device is presented. For the fluid flow equations the stream function-vorticity formulation is adopted, while the lattice Boltzmann method (LBM) is utilized for…
In this paper, we develop an efficient numerical solver for unsteady diffusion-type partial differential equations with random coefficients. A major computational challenge in such problems lies in repeatedly handling large-scale linear…
We propose a low-rank tensor approach to approximate linear transport and nonlinear Vlasov solutions and their associated flow maps. The approach takes advantage of the fact that the differential operators in the Vlasov equation is tensor…
We propose a numerical approach for solving conjugate heat transfer problems using the finite volume method. This approach combines a semi-implicit scheme for fluid flow, governed by the incompressible Navier-Stokes equations, with an…
In this paper a hybridized weak Galerkin (HWG) finite element method for solving the Stokes equations in the primary velocity-pressure formulation is introduced. The WG method uses weak functions and their weak derivatives which are defined…
Dispersion of low-density rigid particles with complex geometries is ubiquitous in both natural and industrial environments. We show that while explicit methods for coupling the incompressible Navier-Stokes equations and Newton's equations…
A D2Q9 Hybrid Lattice Boltzmann Method (HLBM) is proposed for the simulation of both compressible subsonic and supersonic flows. This HLBM is an extension of the model of Feng et al: [12], which has been found, via different test cases, to…