Related papers: A Deep Finite Difference Emulator for the Fast Sim…
In this paper we present a simple and accurate second order finite element scheme to simulate the Burgers' equation on the whole real line and subjected to initial conditions with compact support. The numerical simulations are performed by…
The article focuses on error estimates as well as stability analysis of deep learning methods for stationary and non-stationary viscous Burgers equation in two and three dimensions. The local well-posedness of homogeneous boundary value…
The numerical simulation of the inviscid Burgers' equation is often hindered by spurious oscillations near discontinuities. To mitigate this issue, a viscous term can be introduced, leading to the viscous Burgers' equation. In this work,…
We study a variable-coefficient Burgers equation arising in the modelling of segregation of dry bidisperse granular mixtures. The equation is subject to nonlinear boundary conditions for the particle flux. We construct a strongly implicit…
In this paper, we analyze the three-level explicit time-split MacCormack procedure in the numerical solutions of two-dimensional viscous coupled Burgers' equations subject to initial and boundary conditions. The differential operators split…
In this paper, a numerical solution of the two dimensional nonlinear coupled viscous Burgers equation is discussed with the appropriate initial and boundary conditions using the modified cubic B spline differential quadrature method. In…
Data-driven turbulence modeling is experiencing a surge in interest following algorithmic and hardware developments in the data sciences. We discuss an approach using the differentiable physics paradigm that combines known physics with…
An emulator is a fast-to-evaluate statistical approximation of a detailed mathematical model (simulator). When used in lieu of simulators, emulators can expedite tasks that require many repeated evaluations, such as sensitivity analyses,…
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.…
Real-time simulation of elastic structures is essential in many applications, from computer-guided surgical interventions to interactive design in mechanical engineering. The Finite Element Method is often used as the numerical method of…
Finite element-based high-order solvers of conservation laws offer large accuracy but face challenges near discontinuities due to the Gibbs phenomenon. Artificial viscosity is a popular and effective solution to this problem based on…
We construct a class of infinite mass functions for which solutions of the viscous Burgers equation decay at a better rate than solution of the heat equation for initial data in this class. In other words, we show an enhanced dissipation…
In this paper we use a Variational Quantum Algorithm to solve Initial Value Problems with the Implicit Crank-Nicolson and the Method of Lines (MoL) evolution schemes. The unknown functions use a spectral decomposition with the Fourier…
Dynamic simulators are computational models governed by differential equations that evolve over time. They are essential for scientific and engineering applications but remain challenging to emulate because of the unpredictable behavior of…
In applied sciences, we often deal with deterministic simulation models that are too slow for simulation-intensive tasks such as calibration or real-time control. In this paper, an emulator for a generic dynamic model, given by a system of…
This work proposes an efficient space-time two-grid compact difference (ST-TGCD) scheme for solving the two-dimensional (2D) viscous Burgers' equation subject to initial and periodic boundary conditions. The proposed approach combines a…
In this work, a physics-informed neural networks (PINNs) based algorithm is used for simulation of nonlinear 1D and 2D Burgers' type models. This scheme relies on a neural network built to approximate the problem solution and use a trial…
We revisit the analogy between feed-forward deep neural networks (DNNs) and discrete dynamical systems derived from neural integral equations and their corresponding partial differential equation (PDE) forms. A comparative analysis between…
Simulating the dynamic characteristics of a PN junction at the microscopic level requires solving the Poisson's equation at every time step. Solving at every time step is a necessary but time-consuming process when using the traditional…
Simulation of fluid flows is crucial for modeling physical phenomena like meteorology, aerodynamics, and biomedicine. Classical numerical solvers often require fine spatiotemporal grids to satisfy stability, consistency, and convergence…