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The URANS equations provide a computationally efficient tool to simulate unsteady turbulent flows for a wide range of applications. To account for the errors introduced by the turbulence closure model, recent works have adopted data…
We present reliable a posteriori estimators for some fully discrete schemes applied to nonlinear systems of hyperbolic conservation laws in one space dimension with strictly convex entropy. The schemes are based on a method of lines…
The dynamics of the fluid fields in a large class of causal dissipative fluid theories is studied. It is shown that the physical fluid states in these theories must relax (on a time scale that is characteristic of the microscopic particle…
A class of A.L.E. time discretisations which inherit key energetic properties (nonlinear dissipation in the absence of forcing and long-term stability under conditions of time dependent loading), irrespective of the time increment employed,…
We analyze a semi-explicit time discretization scheme of first order for poro\-elasticity with nonlinear permeability provided that the elasticity model and the flow equation are only weakly coupled. The approach leads to a decoupling of…
The time relaxation model, which is family of high accuracy turbulence models, has proven to be effective in regularization of Navier Stokes Equations. The model belongs to the class of Large Eddy Simulation models, and is derived by adding…
Different relaxation approximations to partial differential equations, including conservation laws, Hamilton-Jacobi equations, convection-diffusion problems, gas dynamics problems, have been recently proposed. The present paper focuses onto…
We present benchmark computations of dynamic poroelasticity modeling fluid flow in deformable porous media by a coupled hyperbolic-parabolic system of partial differential equations. A challenging benchmark setting and goal quantities of…
The incompressible Navier-Stokes equations are solved in a channel, using a Discontinuous Galerkin method over staggered grids. The resulting linear systems are studied both in terms of the structure and in terms of the spectral features of…
In this article we obtain an optimal best approximation type result for fully discrete approximations of the transient Stokes problem. For the time discretization we use the discontinuous Galerkin method and for the spatial discretization…
Solving time-dependent Partial Differential Equations (PDEs) using a densely discretized spatial domain is a fundamental problem in various scientific and engineering disciplines, including modeling climate phenomena and fluid dynamics.…
This paper introduces a novel data-driven convergence booster that not only accelerates convergence but also stabilizes solutions in cases where obtaining a steady-state solution is otherwise challenging. The method constructs a…
Kinetic approaches, i.e., methods based on the lattice Boltzmann equations, have long been recognized as an appealing alternative for solving incompressible Navier-Stokes equations in computational fluid dynamics. However, such approaches…
In this paper, we investigate numerically a diffuse interface model for the Navier-Stokes equation with fluid-fluid interface when the fluids have different densities \cite{Lowengrub1998}. Under minor reformulation of the system, we show…
Combining the characteristic method and the local discontinuous Galerkin method with carefully constructing numerical fluxes, we design the variational formulations for the time-dependent convection-dominated Navier-Stokes equations in…
Computational multi-scale methods capitalize on a large time-scale separation to efficiently simulate slow dynamics over long time intervals. For stochastic systems, one often aims at resolving the statistics of the slowest dynamics. This…
We present a class of new explicit and stable numerical algorithms to solve the spatially discretized linear heat or diffusion equation. After discretizing the space and the time variables like conventional finite difference methods, we do…
In this paper we consider fully discrete approximations with inf-sup stable mixed finite element methods in space to approximate the Navier-Stokes equations. A continuous downscaling data assimilation algorithm is analyzed in which…
Global spectral methods offer the potential to compute solutions of partial differential equations numerically to very high accuracy. In this work, we develop a novel global spectral method for linear partial differential equations on cubes…
Computing solutions to partial differential equations using the fast Fourier transform can lead to unwanted oscillatory behavior. Due to the periodic nature of the discrete Fourier transform, waves that leave the computational domain on one…