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Acceleration Vectors01:30

Acceleration Vectors

In everyday conversation, accelerating means speeding up. Acceleration is a vector in the same direction as the change in velocity, Δv, therefore the greater the acceleration, the greater the change in velocity over a given time. Since velocity is a vector, it can change in magnitude, direction, or both. Thus acceleration is a change in speed or direction, or both. For example, if a runner traveling at 10 km/h due east slows to a stop, reverses direction, and continues their run at 10 km/h due...
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Analyte Adsorption and Distribution01:09

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When an object moves with constant acceleration, the velocity of the object changes at a constant rate throughout the motion. The kinematic equations of motions are derived for such cases where the acceleration of the object is constant. The first kinematic equation gives an insight into the relationship between velocity, acceleration, and time. We can see, for example:

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Updated: May 22, 2026

Multiscale Sampling of a Heterogeneous Water/Metal Catalyst Interface using Density Functional Theory and Force-Field Molecular Dynamics
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Published on: April 12, 2019

Vector Acceleration Methods for Faster Convergence of Cyclic Steady State in Adsorption Process Simulations.

Sai Gokul Subraveti1, Kian Karimi2, Matteo Gazzani2,3

  • 1SINTEF Energy Research, Sem Sælands vei 11, Trondheim 7034, Norway.

Industrial & Engineering Chemistry Research
|May 21, 2026
PubMed
Summary
This summary is machine-generated.

Accelerating simulations of adsorption processes is crucial for efficient separations. Steffensen

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Area of Science:

  • Chemical Engineering
  • Computational Chemistry
  • Separation Science

Background:

  • Simulations of fixed-bed adsorption processes with in situ regeneration are computationally intensive due to repeated nonlinear partial differential equation solutions.
  • Reaching cyclic steady state (CSS) in these simulations requires iterative methods, often leading to significant time consumption and optimization challenges.

Purpose of the Study:

  • To systematically investigate Steffensen's vector acceleration methods for expediting CSS convergence in adsorption process simulations.
  • To evaluate the effectiveness of these methods across diverse adsorption cycle dynamics, including vacuum swing adsorption (VSA), temperature swing adsorption (TSA), and vacuum temperature swing adsorption (VTSA).

Main Methods:

  • Applied variants of Steffensen's vector acceleration methods, specifically noting the Graves-Morris extrapolator.
  • Tested these methods on simulations of a four-step VSA cycle for CO2 capture, a six-step TSA cycle for CO2 capture, and a three-step VTSA cycle for CH4 upgrading.
  • Focused on methods requiring no prior knowledge of first derivatives (Jacobian).

Main Results:

  • Steffensen's methods, particularly the Graves-Morris extrapolator, consistently enhanced CSS convergence rates across all tested adsorption processes.
  • Achieved significant reductions in computational time: up to 75% for VSA, up to 70% for TSA, and up to 35% for VTSA compared to successive substitution.
  • Demonstrated the potential for simple, code-agnostic modifications to accelerate simulations.

Conclusions:

  • Steffensen's vector acceleration methods offer a computationally efficient approach to simulating fixed-bed adsorption processes with in situ regeneration.
  • These methods provide substantial time savings, making simulations and optimization of adsorption-based separations more feasible.
  • The findings highlight a practical strategy for improving the performance of adsorption process modeling.