Positivity preserving high order schemes for angiogenesis models
نویسندگان
چکیده
منابع مشابه
Implicit Positivity-preserving High Order
Positivity-preserving discontinuous Galerkin (DG) methods for solving hyperbolic 5 conservation laws have been extensively studied in the last several years. But nearly all the devel6 oped schemes are coupled with explicit time discretizations. Explicit discretizations suffer from the 7 constraint for the Courant-Friedrichs-Levis (CFL) number. This makes explicit methods impractical 8 for probl...
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Systems in which reaction terms are coupled to diffusion and advection transports arise in a wide range of chemical engineering applications, physics, biology and environmental. In these cases, the components of the unknown can denote concentrations or population sizes which represent quantities and they need to remain positive. Classical finite difference schemes may produce numerical drawback...
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For the initial value problem of scalar conservation laws, a bound-preserving property is desired for numerical schemes in many applications. Traditional methods to enforce a discrete maximum principle by defining the extrema as those of grid point values in finite difference schemes or cell averages in finite volume schemes usually result in an accuracy degeneracy to second order around smooth...
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In [16, 17], we constructed uniformly high order accurate discontinuous Galerkin (DG) schemes which preserve positivity of density and pressure for the Euler equations of compressible gas dynamics with the ideal gas equation of state. The technique also applies to high order accurate finite volume schemes. For the Euler equations with various source terms (e.g., gravity and chemical reactions),...
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ژورنال
عنوان ژورنال: International Journal of Nonlinear Sciences and Numerical Simulation
سال: 2021
ISSN: 2191-0294,1565-1339
DOI: 10.1515/ijnsns-2021-0112