Related papers: Modified (hyper-)viscosity for coarse-resolution o…
The present work aims to revisit the simplifications made in the Navier-Stokes equations for the flow between two cylinders with a small thickness of lubricating oil film. Through a dimensionless analysis, the terms of these equations are…
We address the question of parameterizing the subgrid scales in simulations of geophysical flows by applying stochastic mode reduction to the one-dimensional stochastically forced shallow water equations. The problem is formulated in…
Submesoscale processes, with spatio-temporal scales of O(0.01-10) km and hours to 1 day which are hardly resolved by current ocean models, are important sub-grid processes in ocean models. Due to the strong vertical currents, submesoscale…
The two-scale computational homogenization method is proposed for modelling of locally periodic fluid-saturated media subjected a to large deformation induced by quasistatic loading. The periodic heterogeneities are relevant to the…
Semi-implicit methods are powerful and efficient tools for the three-dimensional modeling of coastal and oceanic processes. A semi-implicit finite difference method for 3D hydrostatic primitive equations is presented in this paper. The…
Methods for model parameter estimation, uncertainty quantification and experimental design are summarized in this paper. They are based on the generalized least squares estimator and different approximations of its covariance matrix using…
In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…
We propose an extension of the discretization approaches for multilayer shallow water models, aimed at making them more flexible and efficient for realistic applications to coastal flows. A novel discretization approach is proposed, in…
Often computational models are too expensive to be solved in the entire domain of simulation, and a cheaper model would suffice away from the main zone of interest. We present for the concrete example of an evolution problem of advection…
In Computational Fluid Dynamics (CFD), coarse mesh simulations offer computational efficiency but often lack precision. Applying conventional super-resolution to these simulations poses a significant challenge due to the fundamental…
The accurate and stable simulation of viscoelastic flows remains a significant computational challenge, exacerbated for flows in non-trivial and practical geometries. Here we present a new high-order meshless approach with variable…
We present a new adaptive resolution technique for efficient particle-based multiscale molecular dynamics (MD) simulations. The presented approach is tailor-made for molecular systems where atomistic resolution is required only in spatially…
This is the second part to our companion paper. The novel method to quantify artificial dissipation proposed in Part 1 is further applied in turbulent channel flow at $\mathrm{Re_\tau}=180$ using various subgrid-scale models, with an…
In this paper, we introduce a new reduced basis methodology for accelerating the computation of large parameterized systems of high-fidelity integral equations. Core to our methodology is the use of coarse-proxy models (i.e., lower…
In this paper, we develop a computational multiscale to solve the parabolic wave approximation with heterogeneous and variable media. Parabolic wave approximation is a technique to approximate the full wave equation. One benefit of the…
This paper puts forth a new large eddy simulation closure modeling strategy for two-dimensional turbulent geophysical flows. This closure modeling approach utilizes approximate deconvolution, which is based solely on mathematical…
Digital modeling of the microstructure is important for studying the physical and transport properties of porous media. Multiscale modeling for porous media can accurately characterize macro-pores and micro-pores in a large-FoV (field of…
We present a method for computing reduced-order models of parameterized partial differential equation solutions. The key analytical tool is the singular value expansion of the parameterized solution, which we approximate with a singular…
In this manuscript, we extend the variational multiscale enrichment (VME) method to model the dynamic response of hyperelastic materials undergoing large deformations. This approach enables the simulation of wave propagation under…
In this work we introduce a viscosity-based notion of solution for general approximation schemes associated with partial differential equations, such as dynamic programming principles~(DPPs). A key feature of our approach is that it…