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The entropy conservative, curvilinear, nonconforming, p-refinement algorithm for hyperbolic conservation laws of Del Rey Fernandez et al. (2019), is extended from the compressible Euler equations to the compressible Navier-Stokes equations.…

In this paper, we study a time discrete scheme for the initial value problem of the ES-BGK kinetic equation. Numerically solving these equations are challenging due to the nonlinear stiff collision (source) terms induced by small mean free…

We consider coupled models for particulate flows, where the disperse phase is made of particles with distinct sizes. We are thus led to a system coupling the incompressible Navier-Stokes equations to the multi-component Vlasov-Fokker-Planck…

This paper presents a joint theoretical and numerical study of a stochastic version of the compressible Navier-Stokes equations within the location uncertainty (LU) framework, applied to problems related to upper ocean vertical mixing. This…

We present a quantitative comparison between two different Implicit-Explicit Runge-Kutta (IMEX-RK) approaches for the Euler equations of gas dynamics, specifically tailored for the low Mach limit. In this regime, a classical IMEX-RK…

A new class of implicit-explicit (IMEX) methods combined with a p-adaptive mixed finite element formulation is proposed to simulate the diffusion of reacting species. Hierarchical polynomial functions are used to construct an…

We consider the compressible Euler system with anelastic scaling, modeling isentropic flows under the influence of gravity. In the zero-Mach-number limit, the solution of the compressible Euler system converges to a variable density…

We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…

Governing equations of motion for a viscous incompressible material surface are derived from the balance laws of continuum mechanics. The surface is treated as a time-dependent smooth orientable manifold of codimension one in an ambient…

In this paper, we present a novel approach to model the fluid/solid interaction forces in a direct solver of the Navier-Stokes equations based on the volume of fluid interface tracking method. The key ingredient of the model is the explicit…

Consistent splitting schemes are among the most accurate pressure segregation methods, incurring no splitting errors or spurious boundary conditions. Nevertheless, their theoretical properties are not yet fully understood, especially when…

Immersed boundary methods simplify mesh generation by embedding the domain of interest into an extended domain that is easy to mesh, introducing the challenge of dealing with cells that intersect the domain boundary. Combined with explicit…

The Navier-Stokes equations are paradigmatic equations describing hydrodynamics of an interacting system with microscopic interactions encoded in transport coefficients. In this work we show how the Navier-Stokes equations arise from the…

This paper addresses how two time integration schemes, the Heun's scheme for explicit time integration and the second-order Crank-Nicolson scheme for implicit time integration, can be coupled spatially. This coupling is the prerequisite to…

Implicit-explicit (IMEX) time stepping methods can efficiently solve differential equa- tions with both stiff and nonstiff components. IMEX Runge-Kutta methods and IMEX linear multistep methods have been studied in the literature. In this…

We propose a structure-preserving scheme for a hybrid model that couples the time-dependent Ginzburg-Landau (TDGL) equation of superconducting vortex dynamics and the nonlinear Bardeen-Cooper-Schrieffer (BCS) gap equation. This formulation…

In this work we construct a high-order Asymptotic-Preserving (AP) Implicit-Explicit (IMEX) scheme for the ES-BGK model for gas mixtures introduced in [Brull, Commun. Math. Sci., 2015]. The time discretization is based on the IMEX strategy…

Vertical equilibrium models have proven to be well suited for simulating fluid flow in subsurface porous media such as saline aquifers with caprocks. However, in most cases the dimensionally reduced model lacks the accuracy to capture the…

This series of papers is devoted to the formulation and the approximation of coupling problems for nonlinear hyperbolic equations. The coupling across an interface in the physical space is formulated in term of an augmented system of…

In this work, we consider the interaction of a 3D incompressible fluid with a 2D flexible shell that occupies (a part of) the boundary of the fluid domain. We assume that the shell is perfectly elastic while the fluid is governed by the…