Related papers: Efficient time stepping for reactive turbulent sim…
We develop a semi-implicit algorithm for time-accurate simulation of the compressible Navier-Stokes equations, with special reference to wall-bounded flows. The method is based on linearization of the partial convective fluxes associated…
To achieve efficient and accurate long-time integration, we propose a fast, accurate, and stable high-order numerical method for solving fractional-in-space reaction-diffusion equations. The proposed method is explicit in nature and…
Chemical reaction systems with a low to moderate number of molecules are typically modeled as discrete jump Markov processes. These systems are oftentimes simulated with methods that produce statistically exact sample paths such as the…
This work proposes novel techniques for the efficient numerical simulation of parameterized, unsteady partial differential equations. Projection-based reduced order models (ROMs) such as the reduced basis method employ a (Petrov-)Galerkin…
The present paper deals with the problem of improving the efficiency of large scale turbulent flow simulations. The high-fidelity methods for modelling turbulent flows become available for a wider range of applications thanks to the…
Astrochemical simulations are a powerful tool for revealing chemical evolution in the interstellar medium. Astrochemical calculations require efficient processing of large matrices for the chemical networks. The large chemical reaction…
We consider the construction of semi-implicit linear multistep methods which can be applied to time dependent PDEs where the separation of scales in additive form, typically used in implicit-explicit (IMEX) methods, is not possible. As…
We present a loosely coupled scheme for the numerical simulation of the cardiac electro-fluid-structure interaction problem, whose solution is typically computationally intensive due to the need to suitably treat the coupling of the…
Spatial stochastic molecular simulations in biology are limited by the intense computation required to track molecules in space either in a discrete time or discrete space framework, meaning that the serial limit has already been reached in…
A widely used strategy to reduce the computational cost in quantum-chemical calculations is to partition the system into an active subsystem, which is the focus of the computational efforts and an environment that is treated at a lower…
We develop an operator splitting method to simulate flows of isothermal compressible natural gas over transmission pipelines. The method solves a system of nonlinear hyperbolic partial differential equations (PDEs) of hydrodynamic type for…
In many applications, the governing PDE to be solved numerically contains a stiff component. When this component is linear, an implicit time stepping method that is unencumbered by stability restrictions is often preferred. On the other…
We propose a quasi-random operator splitting method for evolution equations driven by multiple mechanisms. The method uses a low-discrepancy sequence to generate the ordering of the subflows, while requiring only one application of each…
A fast and accurate computational scheme for simulating nonlinear dynamic systems is presented. The scheme assumes that the system can be represented by a combination of components of only two different types: first-order low-pass filters…
In biochemically reactive systems with small copy numbers of one or more reactant molecules, the dynamics is dominated by stochastic effects. To approximate those systems, discrete state-space and stochastic simulation approaches have been…
We consider the simulation of isentropic flow in pipelines and pipe networks. Standard operating conditions in pipe networks suggest an emphasis to simulate low Mach and high friction regimes -- however, the system is stiff in these regimes…
We explore a class of splitting schemes employing implicit-explicit (IMEX) time-stepping to achieve accurate and energy-stable solutions for thin-film equations and Cahn-Hilliard models with variable mobility. This splitting method…
Various kinetic Monte Carlo algorithms become inefficient when some of the population sizes in a system are large, which gives rise to a large number of reaction events per unit time. Here, we present a new acceleration algorithm based on…
We develop a random batch Ewald (RBE) method for molecular dynamics simulations of particle systems with long-range Coulomb interactions, which achieves an $O(N)$ complexity in each step of simulating the $N$-body systems. The RBE method is…
We present a new splitting method for time-dependent convection-dominated diffusion problems. The original convection diffusion system is split into two sub-systems: a pure convection system and a diffusion system. At each time step, a…