Journal of Computational Physics

• We investigate PINNs framework for full PDE modeling of turbulent convection flows.

The high expressivity and agility of physics-informed neural networks (PINNs) make them promising candidates for full fluid flow PDE modeling. An important question is whether this new paradigm, exempt from the traditional notion of ...

• Real-space formulation and implementation of Kohn-Sham Density Functional Theory suited to twisted geometries.

We present a real-space formulation and implementation of Kohn-Sham Density Functional Theory suited to twisted geometries, and apply it to the study of torsional deformations of X (X = C, Si, Ge, Sn) nanotubes. Our formulation is ...

• Compute two-phase flows with no spurious currents.
• Instead of spurious currents,...

Using current cell-centered numerical methods to calculate two-phase flows result in spurious currents developing at the interface between both phases when the capillary number is low enough. Treatments of the interface such as: ...

• We develop a systematic framework for computing rare event probabilities in stochastic differential equations.

We exploit the relationship between the stochastic Koopman operator and the Kolmogorov backward equation to construct importance sampling schemes for stochastic differential equations. Specifically, we propose using eigenfunctions of ...

• A novel fully decoupled second-order time accurate scheme is developed for the Darcy-Newtonian-Nematic model for two-phase complex fluids.

We consider the numerical approximation of the binary immiscible mixture of nematic liquid crystals and viscous Newtonian fluids confined in a Hele-Shaw cell, where the free interface motion is simulated by using the phase-field ...

• The framework of anti-dissipation pressure correction (APC) is established for Godunov-type schemes.

An effective and unified framework, termed anti-dissipation pressure correction, is established to overcome the deterioration in the accuracy observed in Godunov-type schemes in low-speed scenarios. Based on the scale analysis of the ...

• Freeform optics.
• Reflector design/optimization.

We address the “freeform optics” inverse problem of designing a reflector surface mapping a prescribed source distribution of light to a prescribed far-field distribution, for a finite light source. When the finite source reduces to a ...

This paper develops high-order accurate entropy stable (ES) adaptive moving mesh finite difference schemes for the two- and three-dimensional special relativistic hydrodynamic (RHD) and magnetohydrodynamic (RMHD) equations, which is ...

Conventional particle-in-cell (PIC) methods suffer from enhanced numerical heating (explicit PIC) or cooling (semi-implicit PIC) when coupled with a binary Monte-Carlo algorithm for Coulomb collisions. In this work, a fully-implicit θ-...

• Particle-in-cell.
• Monte-Carlo collisions.

• The Low-Mach accuracy degradation problem is revisited in the context of ES Schemes.

Entropy-Stable (ES) schemes, specifically those built from Tadmor (1987) [54], have been gaining interest over the past decade, especially in the context of under-resolved simulations of compressible turbulent flows using high-order ...

• This paper addresses one unresolved issue for the SAV method.
• It introduces a ...

The scalar auxiliary variable (SAV) method was introduced by Shen et al. in [36] and has been broadly used to solve thermodynamically consistent PDE problems. By utilizing scalar auxiliary variables, the original PDE problems are ...

• Partially-averaged Navier–Stokes implemented in a flux reconstruction framework.

High-order methods and hybrid turbulence models have independently shown promise as means of decreasing the computational cost of scale-resolving simulations. The objective of this work is to develop the combination of these methods ...

• The explicit integrating factor Runge-Kutta methods coupled with nondecreasing abscissa (eIFRK+) are presented.

We extend the explicit integrating factor Runge-Kutta methods coupled with non-decreasing abscissas (eIFRK⁺) to the nonlocal Allen-Cahn (NAC) equation. We further propose the new three-stage third-order and four-stage fourth-order ...

• An efficient computational method for first-principles (DFT) study of crystal defects.

We present an accurate and efficient finite-difference formulation and parallel implementation of Kohn-Sham Density (Operator) Functional Theory (DFT) for non periodic systems embedded in a bulk environment. Specifically, employing non-...

• A parameterized exterior calculus is introduced for learning physics.
• Analysis ...

As traditional machine learning tools are increasingly applied to science and engineering applications, physics-informed methods have emerged as effective tools for endowing inferences with properties essential for physical ...

We propose the use of physics-informed neural networks for solving the shallow-water equations on the sphere in the meteorological context. Physics-informed neural networks are trained to satisfy the differential equations along with ...

• PINNs are trained for the shallow-water equations on the sphere.
• The method is ...

• A solver to simulate two-phase compressible flows is presented.
• A semi-implicit ...

The development of numerical solvers able to simulate compressible two-phase flows is still a great challenge in computational fluid dynamics. The interaction between acoustic waves and interfaces is of major concern for several ...

The isentropic vortex problem is frequently solved to test the accuracy of numerical methods and verify corresponding code. Unfortunately, its existing solution was derived in the relativistic magnetohydrodynamics by numerically ...

• Intrusive generalised Polynomial Chaos (gPC).
• More efficient than non-intrusive ...

In this paper, we are interested in taking into account uncertainties for k eff computations in neutronics. More generally, the material of this paper can be applied to propagate uncertainties in eigenvalue/eigenvector computations for ...

Plasma simulation is getting increasingly important to reproduce technically relevant configurations in electrical engineering. For instance, simulation tools are used to represent the evolution of partial discharges in internal ...

In this paper, we mainly concern with the order reduction for the unknown solution coefficient vectors about the classical continuous space-time finite element (CCSTFE) method of the two-dimensional (2D) non-stationary incompressible ...

• The continuous space-time finite element (CSTFE) method for unsteady Navier-Stokes equations is proposed for the first time.

• Numerical analysis for minimum-entropy moment models with piece-wise linear (continuous and discontinuous) basis functions.

We derive a second-order realizability-preserving scheme for moment models for linear kinetic equations. We apply this scheme to the first-order continuous (HFM n) and discontinuous (PMM n) models in slab and three-dimensional geometry ...

We describe a fourth-order accurate finite-difference time-domain scheme for solving dispersive Maxwell's equations with nonlinear multi-level carrier kinetics models. The scheme is based on an efficient single-step three time-level ...

• A novel scheme for Maxwell's equations and nonlinear active media is developed.

We present a numerical analysis of linear multigrid operators for the high-order Flux Reconstruction method. The non-modal analysis is used to assess the short-term numerical dissipation in the context of 1D and 2D linear convection-...

• Performed a numerical analysis of multigrid for the Flux Reconstruction method.

In this work, by extending the Gurtin-Murdoch surface elasticity theory to a surface hydrodynamics theory, we developed an adhesive surface hydrodynamics theory of moving contact line (MCL), which is essentially a hybrid theory of a ...

• We have developed an adhesive Gurtin-Murdoch surface hydrodynamics theory of moving contact line.