Conservative CIP Method and Application to Splashing Phenomena

2003 ◽  
Author(s):  
Takashi Yabe
Keyword(s):  
Water Surface ◽  
Mass Conservation ◽  
Cip Method ◽  
Exact Mass ◽  
Comprehensive Review ◽  
Numerical Solver ◽  
Multi Phase ◽  
Solid Liquid ◽  
Lagrangian Scheme ◽  
Recent Version

We present a review of the CIP method [1–3] that is known as a general numerical solver for solid, liquid, gas and plasmas. This method is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. The recent version of this method guarantees the exact mass conservation [4] even in the framework of semi-Lagrangian scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and subcell resolution including front capturing algorithm with functional transformation, pressure-based algorithm. In this paper, particular attention is placed on splashing phenomena in which water surface breaks up and disintegrated into many pieces.

Three-Phase Flow Calculation With Conservative Semi-Lagrangian CIP Method

2002 ◽  
Author(s):  
T. Yabe ◽  
F. Xiao ◽  
K. Takizawa ◽  
K. Sakurai
Keyword(s):  
Mass Conservation ◽  
Phase Flow ◽  
Cip Method ◽  
Exact Mass ◽  
Comprehensive Review ◽  
Three Phase ◽  
Three Phase Flow ◽  
Multi Phase ◽  
Lagrangian Scheme ◽  
Recent Version

We present a review of the CIP method, which is a kind of semi-Lagrangian scheme and has been extended to treat incompressible flow in the framework of compressible fluid. Since it uses primitive Euler representation, it is suitable for multi-phase analysis. The recent version of this method guarantees the exact mass conservation even in the framework of semi-Lagrangian scheme. Comprehensive review is given for the strategy of the CIP method that has a compact support and sub-cell resolution including front capturing algorithm with functional transformation.

Lignin waste processing into solid, liquid, and gaseous fuels: a comprehensive review

2021 ◽  
Author(s):  
Shreya Suresh ◽  
Vinatha Viswanathan ◽  
Malarvizhi Angamuthu ◽  
Gnana Prakash Dhakshinamoorthy ◽  
Kannappan Panchamoorthy Gopinath ◽  
...  
Keyword(s):  
Waste Processing ◽  
Comprehensive Review ◽  
Gaseous Fuels ◽  
Solid Liquid

scholarly journals A mimetic, semi-implicit, forward-in-time, finite volume shallow water model: comparison of hexagonal–icosahedral and cubed-sphere grids

2014 ◽  
Vol 7 (3) ◽  
pp. 909-929 ◽  
Author(s):  
J. Thuburn ◽  
C. J. Cotter ◽  
T. Dubos
Keyword(s):  
Shallow Water ◽  
Finite Volume ◽  
Model Comparison ◽  
Mass Conservation ◽  
Time Discretization ◽  
Water Model ◽  
Tracer Transport ◽  
Exact Mass ◽  
Large Wave ◽  
Cubed Sphere

Abstract. A new algorithm is presented for the solution of the shallow water equations on quasi-uniform spherical grids. It combines a mimetic finite volume spatial discretization with a Crank–Nicolson time discretization of fast waves and an accurate and conservative forward-in-time advection scheme for mass and potential vorticity (PV). The algorithm is implemented and tested on two families of grids: hexagonal–icosahedral Voronoi grids, and modified equiangular cubed-sphere grids. Results of a variety of tests are presented, including convergence of the discrete scalar Laplacian and Coriolis operators, advection, solid body rotation, flow over an isolated mountain, and a barotropically unstable jet. The results confirm a number of desirable properties for which the scheme was designed: exact mass conservation, very good available energy and potential enstrophy conservation, consistent mass, PV and tracer transport, and good preservation of balance including vanishing ∇ × ∇, steady geostrophic modes, and accurate PV advection. The scheme is stable for large wave Courant numbers and advective Courant numbers up to about 1. In the most idealized tests the overall accuracy of the scheme appears to be limited by the accuracy of the Coriolis and other mimetic spatial operators, particularly on the cubed-sphere grid. On the hexagonal grid there is no evidence for damaging effects of computational Rossby modes, despite attempts to force them explicitly.

scholarly journals A mass conserving mixed stress formulation for the Stokes equations

2019 ◽  
Vol 40 (3) ◽  
pp. 1838-1874 ◽  
Author(s):  
Jay Gopalakrishnan ◽  
Philip L Lederer ◽  
Joachim Schöberl
Keyword(s):  
Finite Elements ◽  
Degrees Of Freedom ◽  
Stokes Equations ◽  
Computational Cost ◽  
Mass Conservation ◽  
Rates Of Convergence ◽  
Exact Mass ◽  
Conservation Property ◽  
Pressure Independent ◽  
Preservation Property

Abstract We propose stress formulation of the Stokes equations. The velocity $u$ is approximated with $H(\operatorname{div})$-conforming finite elements providing exact mass conservation. While many standard methods use $H^1$-conforming spaces for the discrete velocity $H(\operatorname{div})$-conformity fits the considered variational formulation in this work. A new stress-like variable $\sigma $ equalling the gradient of the velocity is set within a new function space $H(\operatorname{curl} \operatorname{div})$. New matrix-valued finite elements having continuous ‘normal-tangential’ components are constructed to approximate functions in $H(\operatorname{curl} \operatorname{div})$. An error analysis concludes with optimal rates of convergence for errors in $u$ (measured in a discrete $H^1$-norm), errors in $\sigma $ (measured in $L^2$) and the pressure $p$ (also measured in $L^2$). The exact mass conservation property is directly related to another structure-preservation property called pressure robustness, as shown by pressure-independent velocity error estimates. The computational cost measured in terms of interface degrees of freedom is comparable to old and new Stokes discretizations.

Numerical modelling of igneous processes

2021 ◽  
Author(s):  
Tobias Keller
Keyword(s):  
Plate Tectonics ◽  
Experimental Studies ◽  
Computational Modelling ◽  
Mineral Resources ◽  
Transport Processes ◽  
Suspension Flow ◽  
Phase Reaction ◽  
Numerical Application ◽  
Multi Phase ◽  
Solid Liquid

<p>Magma matters. From magmatic differentiation of terrestrial planets into core, mantle and crust, to magmatism modulating plate tectonics and deep volatile cycles that maintain a habitable Earth, and volcanism causing terrible hazards but also providing rich energy and mineral resources – igneous processes are integral to the evolution of Earth and other terrestrial planetary bodies. Our understanding of volcanoes and their deep magmatic roots derives from a range of disciplines including field geology, experimental petrology, geochemical analyses, geophysical imaging, and volcano monitoring. Observational and experimental studies, however, are hampered by incomplete access to processes that play out across scales ranging from sub-millimetre size to thousands of kilometres, and from seconds to billions of years. Computational modelling provides a tool kit for investigating igneous processes across these scales.</p><p>Over the past decade, my research has been focused on advancing the theoretical description and numerical application of multi-phase reaction-transport processes at the volcano to planetary scale. Mixture theory provides a framework to represent the spatially averaged behaviour of a large sample of microscopic phase constituents including mineral grains, melt films, fluid droplets, and vapour bubbles. The approach has been used successfully to model both porous flow of melt percolating through compacting rock, as well as suspension flow of crystals settling in convecting magma bodies. My recent work has introduced a new modelling framework that bridges the porous to mushy and suspension flow limits, and extends beyond solid-liquid systems to multi-phase systems including several solid, liquid, and vapour phases. Igneous process modelling can thus provide new insights into the generation and extraction of mantle melts, the dynamics of crustal magma processing, the outgassing and eruption of shallow magma reservoirs, and the generation of mineral resources by exsolution of enriched magmatic liquids.</p>

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