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[[File:Staggered methodology for software coupling.png|thumb|Staggered methodology for discrete/continuous applications.]]
NumerousMany challengesengineering in engineeringproblems exist and evolve, that include a continuous and discrete phase simultaneouslyphases, and therefore,those problems cannot be solvedsimulated accurately by continuous or discrete approaches, only. Therefore, XDEM provides a platform, that couples discrete and continuous phasessolution for asome largeof number ofthose engineering applications.
Although research and development of numerical methods in each domains of discrete and continuous solvers is still progressing, respective software tools haveare reached a high degree of maturityavailable. In order to couple discrete and continuous approaches, two major conceptsapproaches are available:
*'''Monolithic conceptapproach''': The equations describing multi-physics phenomena are solved simultaneously by a single solver producing a complete solution.
*'''Partitioned or staggered conceptapproach''': The equations describing multi-physics phenomena are solved sequentially by appropriately tailored and distinct solvers with passing the results of one analysis as a load to the nextother.
The former conceptapproach requires a solver that includes a combination ofhandles all physical problems involved, and therefore, it requires a largelarger implementation effort. However, there exist scenarios for which it is difficult to arrange the coefficients of combined [[differential equations]] in one [[Matrix (mathematics)|matrix]]. A partitioned concept as a coupling between a number of solvers representing individual domains of physics offers distinctive advantages over a monolithic concept.
The latter, partitioned, approach couples a number of solvers representing individual domains of physics offers advantages over a monolithic concept. It encompasses a larger degree of flexibility because it can use many solvers. Furthermore, it allows a more modular software development. However, partitioned simulations require stable and accurate coupling algorithms.
It inherently encompasses a large degree of flexibility by coupling an almost arbitrary number of solvers.
Within the staggered concept of XDEM, continuous fields are described by the solution the respective continuous (conservation) equations. Properties of individual particles such as temperature are also resolved by solving respective conservation equations that yieldsyield both a spatial and temporal internal distribution of relevant variables. MayorMajor conservation principles with their equations and variables to be solved for and that are employed to an individual particle within XDEM are listed in the following table.▼Furthermore, a more modular software development is retained that allows by far more specific solver techniques adequate to the
problems addressed. However, partitioned simulations impose stable and accurate coupling algorithms that convince by their pervasive character.
▲Within the staggered concept of XDEM, continuous fields are described by the solution the respective continuous (conservation) equations. Properties of individual particles such as temperature are also resolved by solving respective conservation equations that yields both a spatial and temporal internal distribution of relevant variables. Mayor conservation principles with their equations and variables to be solved for and that are employed to an individual particle within XDEM are listed in the
following table.
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