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We adapt a symmetric interior penalty discontinuous Galerkin method using a patch reconstructed approximation space to solve elliptic eigenvalue problems, including both second and fourth order problems in 2D and 3D. It is a direct…
Functional integral representations for solutions of the motion equations for wall-bounded incompressible viscous flows, expressed (implicitly) in terms of distributions of solutions to stochastic differential equations of McKean-Vlasov…
This work proposes a statistically enhanced framework to address the instability and limited predictive capability of conventional Galerkin-Proper Orthogonal Decomposition (Galerkin-POD) models. The method reformulates the correction of the…
The bounded oscillations of rotating fluid-filled ellipsoids can provide physical insight into the flow dynamics of deformed planetary interiors. The inertial modes, sustained by the Coriolis force, are ubiquitous in rapidly rotating fluids…
High-order Discontinuous Galerkin Spectral Element Methods (DGSEM) provide excellent accuracy for complex flow simulations, but their computational cost increases sharply with higher polynomial orders. %that provide very accurate solutions.…
A discontinuous Galerkin method by patch reconstruction is proposed for Stokes flows. A locally divergence-free reconstruction space is employed as the approximation space, and the interior penalty method is adopted which imposes the normal…
In recent years several research efforts focused on the development of high-order discontinuous Galerkin (dG) methods for scale resolving simulations of turbulent flows. Nevertheless, in the context of incompressible flow computations, the…
We formulate and analyze interior penalty discontinuous Galerkin methods for coupled elliptic PDEs modeling excitable tissue, represented by intracellular and extracellular domains sharing a common interface. The PDEs are coupled through a…
This paper introduces well-balanced path-conservative discontinuous Galerkin (DG) methods for two-layer shallow water equations, ensuring exactness for both still water and moving water equilibrium steady states. The approach involves…
In this study, we propose a unified, general framework for the direct discontinuous Galerkin methods. In the new framework, the antiderivative of the nonlinear diffusion matrix is not needed. This allows a simple definition of the numerical…
The high-order accurate continuous Galerkin finite element method offers attractive computational efficiency for computational fluid dynamics. A challenge is however spurious oscillations which result for convection dominated flows over…
Modeling flow in geosystems with natural fault is a challenging problem due to low permeability of fault compared to its surrounding porous media. One way to predict the behavior of the flow while taking the effects of fault into account is…
We discuss the development, verification, and performance of a GPU accelerated discontinuous Galerkin method for the solutions of two dimensional nonlinear shallow water equations. The shallow water equations are hyperbolic partial…
We propose a new method, the continuous Galerkin method with globally and locally supported basis functions (CG-GL), to address the parametric robustness issues of reduced-order models (ROMs) by incorporating solution-based adaptivity with…
We consider the impingement of a droplet onto a wall with high impact speed. To model this process we favour a diffuse-interface concept. Precisely, we suggest a compressible Navier--Stokes--Allen--Cahn model. Basic properties of the model…
The diffusive-viscous wave equation is an advancement in wave equation theory, as it accounts for both diffusion and viscosity effects. This has a wide range of applications in geophysics, such as the attenuation of seismic waves in…
Modeling flow through porous media with multiple pore-networks has now become an active area of research due to recent technological endeavors like geological carbon sequestration and recovery of hydrocarbons from tight rock formations.…
We develop a stochastic Galerkin method for a coupled Navier-Stokes-cloud system that models dynamics of warm clouds. Our goal is to explicitly describe the evolution of uncertainties that arise due to unknown input data, such as model…
In this paper, we apply a specifically designed dissipative spatial filter as sub-grid scale model within the increasingly popular discontinuous Galerkin methods and the closely related flux reconstruction high order methods for large eddy…
We present a high-order hybridizable discontinuous Galerkin method for the numerical solution of time-dependent three-phase flow in heterogeneous porous media. The underlying algorithm is a semi-implicit operator splitting approach that…