By F. Moukalled, L. Mangani, M. Darwish
ISBN-10: 3319168738
ISBN-13: 9783319168739
ISBN-10: 3319168746
ISBN-13: 9783319168746
This textbook explores either the theoretical beginning of the Finite quantity process (FVM) and its functions in Computational Fluid Dynamics (CFD). Readers will find a thorough clarification of the FVM numerics and algorithms used for the simulation of incompressible and compressible fluid flows, in addition to a close exam of the elements wanted for the improvement of a collocated unstructured pressure-based CFD solver. specific CFD codes are explored. the 1st is uFVM, a three-d unstructured pressure-based finite quantity educational CFD code, applied inside Matlab. the second one is OpenFOAM®, an open resource framework utilized in the advance of various CFD courses for the simulation of business scale movement problems.
With over 220 figures, a number of examples and a couple of hundred workout on FVM numerics, programming, and functions, this textbook is appropriate to be used in an introductory direction at the FVM, in a complicated path on numerics, and as a reference for CFD programmers and researchers.
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Additional resources for The finite volume method in computational fluid dynamics : an advanced introduction with OpenFOAM® and Matlab®
Example text
Moreover, rs is normal to the constant s surface that passes through that point. 16 2 z l Review of Vector Calculus directional ds = = s el derivative dl s s = s ( x, y, z ) el C k i j y x Fig. 7 The rate of change of sðx; y; zÞ in the direction of vector el Example 3 Let f ðx; y; zÞ ¼ x2 y þ y2 z þ z2 x (a) find rf at point ð3; 2; 0Þ. 7 Operations on the Nabla Operator The dot product of the del operator with a vector v of components u; v; and w in the x; y; and z direction, respectively, results in the divergence of the vector [7, 8], which is a scalar quantity written as rÁv¼ @u @v @w þ þ @x @y @z ð2:20Þ Physically the divergence of a vector field over a region is a measure of how much the vector field points into or out of the region.
The first term on the right side gives the change in the integral because / is changing with time t, while the second and third terms accounts for the gain and loss in area as the upper and lower bounds are moved, respectively. 38 2 Review of Vector Calculus ( x,t + t ) Term I ( x,t ) Term III Term II a (t ) a (t + t ) b(t ) b(t + t ) t Fig. 18 Curves showing the spatial distribution of a function at times t and t þ Dt The three-dimensional form of this formula applied to a volume V ðtÞ enclosed by a surface SðtÞ with its surface elements moving with a velocity vs can be written as d dt Z /dV ¼ Z @/ dV þ @t V ðtÞ V ðt Þ Z /ðvs Á nÞdS ð2:88Þ SðtÞ where /ðt; xÞ is a scalar function of space and time.
4 Divergence Theorem Let V represents a volume in three-dimensional space (Fig. 17) of boundary S. Let n be the outward pointing unit vector normal to S. , the volume integral of its divergence) over the region inside the surface. It is an important theorem for fluid dynamics. 36 2 Fig. 17 A volume in three-dimensional space with a piecewise smooth boundary S Review of Vector Calculus z S dS dS = ndS y v V x The divergence theorem can be used in different contexts to derive many other useful identities (corollaries) [32].
The finite volume method in computational fluid dynamics : an advanced introduction with OpenFOAM® and Matlab® by F. Moukalled, L. Mangani, M. Darwish
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