Related papers: Dissipation-Based Continuation Method for Multipha…
We present a discrete exterior calculus (DEC) based discretization scheme for incompressible two-phase flows. Our physically-compatible exterior calculus discretization of single phase flow is extended to simulate immiscible two-phase flows…
A method for post-processing the velocity after a pressure projection is developed that helps to maintain stability in an under-resolved, inviscid, discontinuous element-based simulation for use in environmental fluid mechanics process…
We study a dissipative system of nonlinear and nonlocal equations modeling the flow of electrohydrodynamics. The existence, uniqueness and regularity of solutions is proven for general $\mathbf{L}^2$ initial data in two space dimensions and…
We propose certain approach of solving two-dimensional non-stationary and stationary advection-diffusion-reaction boundary value problems through their reduction to the set of corresponding one-dimensional problems. This method leverages…
The numerical simulation of multiphase flows involving dispersed components with large scale disparities, such as the collisions between millimeter-sized bubbles and micron-sized mineral particles in flotation, poses a significant…
This paper extends the previously reported theory of dissipation pathways [J. Chem. Phys. 160, 214111 (2024)] to incorporate off-diagonal subsystem-bath coupling, which is often required to model molecular systems where the environment…
We analyse numerical errors (dissipation and dispersion) introduced by the discretisation of inviscid and viscous terms in energy stable discontinuous Galerkin methods. First, we analyse these methods using a linear von Neumann analysis…
Comparing with the classical local gradient flow and phase field models, the nonlocal models such as nonlocal Cahn-Hilliard equations equipped with nonlocal diffusion operator can describe more practical phenomena for modeling phase…
We present efficient deep learning techniques for approximating flow and transport equations for both single phase and two-phase flow problems. The proposed methods take advantages of the sparsity structures in the underlying discrete…
This paper solves the discretised multiphase flow equations using tools and methods from machine-learning libraries. The idea comes from the observation that convolutional layers can be used to express a discretisation as a neural network…
Multiphase flows frequently occur in many important engineering and scientific applications, but modeling of such flows is a rather challenging task due to complex interfacial dynamics between different phases, let alone if the flow is…
Efficiently computable stability and performance analysis of nonlinear systems becomes increasingly more important in practical applications. Dissipativity can express stability and performance jointly, but existing results are limited to…
Recent advances have shown that the circuit simulation algorithms that allow for solving highly nonlinear circuits of over one billion variables can be applicable to power system simulation and optimization problems through the use of an…
We present a novel combination of numerical techniques to improve the efficiency, accuracy, and robustness of multi-component compressible flow simulations. At the core of our approach is an Entropy-Stable formulation that preserves kinetic…
We present a new method for the approximate solution of the strongly coupled, nonlinear stress-diffusion problem that appears when modeling hydrogen transport in metals. The most salient feature of the proposed approximation is that it is…
Modeling and simulation of multiphase flows in complex geomerties are challenging due to the complexity in describing the interface topology changes among different phases and the difficulty in implementing the boundary conditions on the…
High order methods based on diagonal-norm summation by parts operators can be shown to satisfy a discrete conservation or dissipation of entropy for nonlinear systems of hyperbolic PDEs. These methods can also be interpreted as nodal…
In this work we propose a nonlinear stabilization technique for convection-diffusion-reaction and pure transport problems discretized with space-time isogeometric analysis. The stabilization is based on a graph-theoretic artificial…
A mixed mimetic spectral element method is applied to solve the rotating shallow water equations. The mixed method uses the recently developed spectral element histopolation functions, which exactly satisfy the fundamental theorem of…
We study efficient simulation of steady state for rarefied gas flow, which is modeled by the Boltzmann equation with BGK-type collision term. A nonlinear multigrid solver is proposed to resolve the efficiency issue by the following…