Do Current Lattice Boltzmann Methods for Diffusion and Advection-Diffusion Equations Respect Maximum Principle and the Non-Negative Constraint?
نویسندگان
چکیده
منابع مشابه
Do current lattice Boltzmann methods for diffusion and diffusion-type equations respect maximum principles and the non-negative constraint?
The lattice Boltzmann method (LBM) has established itself as a valid numerical method in computational fluid dynamics. Recently, multiple-relaxation-time LBM has been proposed to simulate anisotropic advection-diffusion processes. The governing differential equations of advective-diffusive systems are known to satisfy maximum principles, comparison principles, the non-negative constraint, and t...
متن کاملDo Current Lattice Boltzmann Methods for Diffusion andAdvection-Diffusion Equations Respect MaximumPrinciple and theNon-Negative Constraint?
The Lattice Boltzmann Method (LBM) has established itself as a popular numerical method in computational fluid dynamics. Several advancements have been recently made in LBM, which include multiple-relaxation-time LBM to simulate anisotropic advection-diffusion processes. Because of the importance of LBM simulations for transport problems in subsurface and reactive flows, one needs to study the ...
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Transient diffusion equations arise in many branches of engineering and applied sciences (e.g., heat transfer and mass transfer), and are parabolic partial differential equations. It is well-known that, under certain assumptions on the input data, these equations satisfy important mathematical properties like maximum principles and the non-negative constraint, which have implications in mathema...
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Mass transport, such as movement of phosphorus in soils and solutes in rivers, is a natural phenomenon and its study plays an important role in science and engineering. It is found that there are numerous practical diffusion phenomena that do not obey the classical advection-diffusion equation (ADE). Such diffusion is called abnormal or superdiffusion, and it is well described using a fractiona...
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Predictive simulations are crucial for the success of many subsurface applications, and it is highly desirable to obtain accurate non-negative solutions for transport equations in these numerical simulations. To this end, optimization-based methodologies based on quadratic programming (QP) have been shown to be a viable approach to ensuring discrete maximum principles and the non-negative const...
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ژورنال
عنوان ژورنال: Communications in Computational Physics
سال: 2016
ISSN: 1815-2406,1991-7120
DOI: 10.4208/cicp.181015.270416a