A Second-order Time-Accurate Unconditionally Stable Method for a Gradient Flow for the Modica–Mortola Functional

Ham, Seokjun; Kwak, Soobin; Lee, Chaeyoung; Lee, Gyeonggyu; Kim, Junseok

doi:10.1007/s10915-023-02198-2

Cited by 2 publications

(2 citation statements)

References 23 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the future, we will apply a least-squares method to find optimal parameter values. 49 Also, to visualize the effect of N 2 O and O 2 on the pressure profiles inside the blood capillary, we illustrate the profiles in Figure 15 at T ¼ 1, 3, and 5. We can see that pressure profiles align with the results presented in Figure 14.…”

Section: Analysis Of the Effect Of Nitrous Oxide (N 2 O) And Oxygen (...mentioning

confidence: 99%

See 1 more Smart Citation

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method

Jyoti,

Kwak,

Ham

et al. 2024

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

This study aims to investigate how inert gas affects the partial pressure of alveolar and venous blood using a fast and accurate operator splitting method (OSM). Unlike previous complex methods, such as the finite element method (FEM), OSM effectively separates governing equations into smaller sub‐problems, facilitating a better understanding of inert gas transport and exchange between blood capillaries and surrounding tissue. The governing equations were discretized with a fully implicit finite difference method (FDM), which enables the use of larger time steps. The model employed partial differential equations, considering convection‐diffusion in blood and only diffusion in tissue. The study explores the impact of initial arterial pressure, breathing frequency, blood flow velocity, solubility, and diffusivity on the partial pressure of inert gas in blood and tissue. Additionally, the effects of anesthetic inert gas and oxygen on venous blood partial pressure were analyzed. Simulation results demonstrate that the high solubility and diffusivity of anesthetic inert gas lead to its prolonged presence in blood and tissue, resulting in lower partial pressure in venous blood. These findings enhance our understanding of inert gas interaction with alveolar/venous blood, with potential implications for medical diagnostics and therapies.

show abstract

Section: Analysis Of the Effect Of Nitrous Oxide (N 2 O) And Oxygen (...mentioning

confidence: 99%

“…We describe the proposed solution algorithm by using the operator splitting method. 49,50 • Step 1: Discretization in r-direction, First we consider the r-direction equation for k ¼ 1 and i ¼ 1, …, N r . Since P Let us consider the continuous flux condition defined in Equation ( 13):…”

Section: Analysis Of the Effect Of Nitrous Oxide (N 2 O) And Oxygen (...mentioning

confidence: 99%

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method

Jyoti,

Kwak,

Ham

et al. 2024

Numer Methods Biomed Eng

Self Cite

View full text Add to dashboard Cite

show abstract

Positivity preserving and unconditionally stable numerical scheme for the three-dimensional modified Fisher–Kolmogorov–Petrovsky–Piskunov equation

Kang,

Kwak,

Hwang

et al. 2025

Journal of Computational and Applied Mathematics

View full text Add to dashboard Cite

A Second-order Time-Accurate Unconditionally Stable Method for a Gradient Flow for the Modica–Mortola Functional

Cited by 2 publications

References 23 publications

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method

Analysis of the effect of inert gas on alveolar/venous blood partial pressure by using the operator splitting method

Positivity preserving and unconditionally stable numerical scheme for the three-dimensional modified Fisher–Kolmogorov–Petrovsky–Piskunov equation

Contact Info

Product

Resources

About