scholarly journals A positivity-preserving high-order weighted compact nonlinear scheme for compressible gas-liquid flows

2021 ◽  
pp. 110569
Author(s):  
Man Long Wong ◽  
Jordan B. Angel ◽  
Michael F. Barad ◽  
Cetin C. Kiris
Keyword(s):  
High Order ◽  
Positivity Preserving ◽  
Liquid Flows ◽  
Compressible Gas

scholarly journals Positivity preserving high order schemes for angiogenesis models

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
A. Carpio ◽  
E. Cebrian
Keyword(s):  
Kinetic Equation ◽  
Time Discretization ◽  
Strong Stability ◽  
High Order ◽  
Angiogenic Factor ◽  
Strong Stability Preserving ◽  
Positivity Preserving ◽  
Blood Vessel Formation ◽  
High Order Schemes ◽  
Asymptotic Reduction

Abstract Hypoxy induced angiogenesis processes can be described by coupling an integrodifferential kinetic equation of Fokker–Planck type with a diffusion equation for the angiogenic factor. We propose high order positivity preserving schemes to approximate the marginal tip density by combining an asymptotic reduction with weighted essentially non oscillatory and strong stability preserving time discretization. We capture soliton-like solutions representing blood vessel formation and spread towards hypoxic regions.

scholarly journals Multidimensional Vlasov–Poisson Simulations with High-order Monotonicity- and Positivity-preserving Schemes

2017 ◽  
Vol 849 (2) ◽  
pp. 76 ◽  
Author(s):  
Satoshi Tanaka ◽  
Kohji Yoshikawa ◽  
Takashi Minoshima ◽  
Naoki Yoshida
Keyword(s):  
High Order ◽  
Positivity Preserving

scholarly journals A High Order Positivity Preserving DG Method for Coagulation-Fragmentation Equations

2019 ◽  
Vol 41 (3) ◽  
pp. B448-B465
Author(s):  
Hailiang Liu ◽  
Robin Gröpler ◽  
Gerald Warnecke
Keyword(s):  
High Order ◽  
Positivity Preserving ◽  
Dg Method

High-order finite difference WENO schemes with positivity-preserving limiter for correlated random walk with density-dependent turning rates

2015 ◽  
Vol 25 (08) ◽  
pp. 1553-1588 ◽  
Author(s):  
Yan Jiang ◽  
Chi-Wang Shu ◽  
Mengping Zhang
Keyword(s):  
Random Walk ◽  
Finite Difference ◽  
Temporal Integration ◽  
Time Discretization ◽  
High Order ◽  
Correlated Random Walk ◽  
Third Order ◽  
Positivity Preserving ◽  
Fifth Order ◽  
High Order Finite Difference

In this paper, we discuss high-order finite difference weighted essentially non-oscillatory schemes, coupled with total variation diminishing (TVD) Runge–Kutta (RK) temporal integration, for solving the semilinear hyperbolic system of a correlated random walk model describing movement of animals and cells in biology. Since the solutions to this system are non-negative, we discuss a positivity-preserving limiter without compromising accuracy. Analysis is performed to justify the maintenance of third-order spatial/temporal accuracy when the limiters are applied to a third-order finite difference scheme and third-order TVD-RK time discretization for solving this model. Numerical results are also provided to demonstrate these methods up to fifth-order accuracy.

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