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We propose a high order discontinuous Galerkin (DG) method for solving nonlinear Fokker-Planck equations with a gradient flow structure. For some of these models it is known that the transient solutions converge to steady-states when time…
Discontinuous Galerkin (DG) discretizations with exact representation of the geometry and local polynomial degree adaptivity are revisited. Hybridization techniques are employed to reduce the computational cost of DG approximations and…
A high-order quasi-conservative discontinuous Galerkin (DG) method is proposed for the numerical simulation of compressible multi-component flows. A distinct feature of the method is a predictor-corrector strategy to define the grid…
For helical isotropic turbulence, an improved two-term helical subgrid-scale (SGS) model is proposed and four types of dynamic methods are given to do large-eddy simulation (LES), which include the standard dynamic procedure, the least…
High-order methods are well-suited for the numerical simulation of complex compressible turbulent flows, but require additional stabilization techniques to capture instabilities arising from the underlying non-linear hyperbolic equations.…
In this paper, we propose a class of non-oscillatory, entropy-stable discontinuous Galerkin (NOES-DG) schemes for solving hyperbolic conservation laws. By incorporating a specific form of artificial viscosity, our new scheme directly…
We extend the data-assimilation approach of Ling and Lozano-Dur\'an (AIAA 2025-1280) to develop machine-learning-based subgrid-scale stress (SGS) models for large-eddy simulation (LES) that are consistent with the numerical scheme of the…
The dynamic model for large-eddy simulation (LES) of turbulent flows requires test filtering the resolved velocity fields in order to determine model coefficients. However, test filtering is costly to perform in large-eddy simulation of…
Discrete dislocation dynamics (DDD) is a widely employed computational method to study plasticity at the mesoscale that connects the motion of dislocation lines to the macroscopic response of crystalline materials. However, the…
Accurate representation of vertical turbulent fluxes is crucial for numerical ocean modelling, both in global and coastal applications. The state-of-the-art approach is to use two-equation turbulence closure models which introduces two…
We developed a novel autonomously dynamic nonlocal turbulence model for the large and very large eddy simulation (LES, VLES) of the homogeneous isotropic turbulent flows (HIT). The model is based on a generalized (integer-to-noninteger)…
Unstructured grid ocean models are advantageous for simulating the coastal ocean and river-estuary-plume systems. However, unstructured grid models tend to be diffusive and/or computationally expensive which limits their applicability to…
High-dimensional PDEs have been a longstanding computational challenge. We propose to solve high-dimensional PDEs by approximating the solution with a deep neural network which is trained to satisfy the differential operator, initial…
The accuracy and computational cost of a large eddy simulation are highly dependent on the computational grid. Building optimal grids manually from a priori knowledge is not feasible in most practical use cases; instead, solution-adaptive…
The problem of an accurate Eulerian-Lagrangian modeling of inertial particle dispersion in Large Eddy Simulation (LES) of turbulent wall-bounded flows is addressed. We run Direct Numerical Simulation (DNS) for turbulent channel flow at…
A previously developed modeling procedure for large eddy simulations (LESs) is extended to allow physical space implementations for inhomogeneous flows. The method is inspired by the well-established theoretical analyses and numerical…
In this paper, we present an entropy-stable (ES) discretization using a nodal discontinuous Galerkin (DG) method for the ideal multi-ion magneto-hydrodynamics (MHD) equations. We start by performing a continuous entropy analysis of the…
In recent years, deep learning methods, exemplified by Physics-Informed Neural Networks (PINNs), have been widely applied to the numerical solution of differential equations. However, these methods may suffer from limited accuracy, high…
We present two families of sub-grid scale (SGS) turbulence models developed for large-eddy simulation (LES) purposes. Their development required the formulation of physics-informed robust and efficient Deep Learning (DL) algorithms which,…
Design of modern nanostructured semiconductor devices often calls for simulation tools capable of modeling arbitrarily-shaped multiscale geometries. In this work, to this end, a discontinuous Galerkin (DG) method-based framework is…