Qualification: 
Ph.D, MPhil, MSc
b_venkatesh@blr.amrita.edu
Phone: 
9036399837

Dr. B. Venkatesh currently serves as Associate Professor and Head of the Department of Mathematics at the School of Engineering, Amrita Vishwa Vidyapeetham, Bengaluru Campus. He was conferred with a Ph. D. in Mathematics, Central College, Bangalore University, Bengaluru. Prior to joining Amrita, he served as Senior Lecturer and Lecturer at The Oxford College of Engineering and BTL Institute of Technology respectively. He has a teaching experience of 19 years.

Education

  • 2006: Ph.D. in Mathematics
    Bangalore University, Karnataka 
  • 2008: M.Phil. in Mathematics
    Bangalore University, Karnataka
  • 2004: B.Sc. in Physics, Mathematics and Instrumentation
    Bangalore University, Karnataka

Professional Appointments

Year Affiliation
Since 2005 Associate Professor and Head, Department of Mathematics, Amrita Vishwa Vidyapeetham, Bengaluru 
1998 - 2002 Lecturer, B T L Institute of Technology, Bangalore
2002 - 2005 Senior Lecturer, The Oxford Institute of Technology, Bangalore

Membership in Professional Bodies

  • Member of (ISTAM)

Certificates, Awards & Recognitions

  • Awarded Best Teacher in B T L Institute of Technology, Bengaluru, Karnataka.

Research Grants Received

Year Funding Agency Title of the Project Investigators Status
2021 NBHM Finite Element Solution of Partial Differential Equations Using New Higher Order Triangular Elements Dr. B. Venkatesh, Dr. Kesavulu Naidu, Dr. Murali K. Ongoing
2015 NBHM Computer Aided Study of Numerical Methods and Graph Labeling Problems Dr. B. Venkatesh, Dr. K. N. Meera Completed

Courses Taught

  • Matrix Algebra
  • Calculus
  • Vector Calculus
  • Linear Algebra
  • Probability and Statistics
  • Integral Transforms
  • Ordinary Differential Equations
  • Partial Differential Equations
  • Numerical Methods
  • Numerical Solution of Differential Equations.

Student Guidance

Sl. No. Name of the Student (s)  Topic Status – Ongoing/Completed
2021 Mamatha T. M. Numerical Methods Ongoing
2015 Shylaja G. Finite Element Methods Ongoing

 

Publications

Publication Type: Journal Article

Year of Publication Title

2019

G. Shylaja, Dr. B. Venkatesh, and Dr. V. Kesavulu Naidu, “Finite Element Method to Solve Poisson’s Equation Using Curved Quadratic Triangular Elements”, IOP Conference Series: Materials Science and Engineering, vol. 577, p. 012165, 2019.[Abstract]


The paper discusses the finite element method to solve Poisson’s equation using quadratic order curved triangular elements. We use quadratic order point transformation to solve the partial differential equation. We observe that with quadratic order as the discretization of the domain element is increased, the error of the solution decreases.

More »»

2019

K. Murali, Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “Darcy–Brinkman–Forchheimer flow over irregular domain using finite elements method”, IOP Conference Series: Materials Science and Engineering, vol. 577, p. 012158, 2019.[Abstract]


The finite element method of solution with curved triangles to solve the three-dimensional, fully-developed Darcy–Brinkman–Forchheimer flow equation in channel with curved side is solved using quasi-linearization and Gauss-Seidel iteration method. Exhaustive numerical computation and numerical experimentation reveals the parameters’ influence on the velocity distributions.. A salient feature of the method adopted in the present paper is that it ensures that the errors are almost equally distributed among all the nodes. It is found that the irregular cross-section channel with upward concave boundary decelerates the flow. Numerical experimentation involved different order curved triangular elements and extensive computation revealed that the quintic order curved triangular element yields the desired solution to an accuracy of 10−5. The finite element method is found to be very effective in capturing boundary and inertia effects in the three-dimensional, fully-developed flow through porous media. Further, it succeeds in giving the required solution for large values of Forchheimer number when shooting method fails to do so. The method can be easily employed in any other irregular cross-section channel.

More »»

2019

T. M. Mamatha and Dr. B. Venkatesh, “Numerical Integration over arbitrary Tetrahedral Element by transforming into standard 1-Cube”, IOP Conference Series: Materials Science and Engineering, vol. 577, p. 012172, 2019.[Abstract]


In this paper, we are using two different transformations to transform the arbitrary linear tetrahedron element to a standard 1-Cube element and obtain the numerical integration formulas over arbitrary linear tetrahedron element implementing generalized Gaussian quadrature rules, with minimum computational time and cost. We also obtain the integral value of some functions with singularity over arbitrary linear tetrahedron region, without discretizing the tetrahedral region into P3 tetrahedral regions. It may be noted the computed results are converging faster than the numerical results in referred articles and are exact for up to 15 decimal values with minimum computational time. In a tetrahedral sub-atomic geometry, a focal particle is situated at the middle with four substituents that are situated at the sides of a tetrahedron. The bond edges are cos−1(−⅓) = 109.4712206…° ≈ 109.5° when each of the four substituents are the same, as in methane(CH4) and in addition its heavier analogs. The impeccably symmetrical tetrahedron has a place with point amass Td, yet most tetrahedral particles have brought down symmetry. Tetrahedral atoms can be chiral. Mathematically the problem is to evaluate the volume integral over an arbitrary tetrahedron transforming the triple integral over arbitrary linear tetrahedron into the integrals over a standard 1-cube using two different parametric transformations.

More »»

2019

Dr. K. Murali, Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “Solution of Darcy-Brinkman Flow Over an Irregular Domain by Finite Element Method”, Journal of Physics: Conference Series, vol. 1172, p. 012091, 2019.[Abstract]


The problem of finding the numerical solution for the flow through a sporadic geometry includes a considerable measure of calculation time. In this article a finite element approach which involves sub-parametric finite element technique with bended triangular elements and with less number of degrees of freedom is used for finding solution of Darcy Brinkman flow through a rectangular duct with one bended side. This reduces the computational time considerably. The showing of the viability of the strategy is the target in this article. Results acquired are in great concurrence with the previous works that has been carried out.

More »»

2018

Dr. K. Murali, V. Naidu, K., and Dr. B. Venkatesh, “Optimal subparametric finite element approach for a Darcy-Brinkman fluid flow problem through a rectangular channel with one curved side”, IOP Conference Series: Materials Science and Engineering, vol. 310, p. 012145, 2018.[Abstract]


In this paper a sub-parametric finite element method is used to find solution of Darcy Brinkman flow through a rectangular channel with one curved side using curved triangular elements. Finding the numerical solution for the flow through a irregular geometry involves a lot of computation time. In order to solve the flow problem with a much effective computational process, a finite element approach with curved triangular elements and with less number of degrees of freedom is employed. The demonstration of the effectiveness of the method is the objective of the paper. Results obtained are in good agreement with previous works done.

More »»

2018

T. M. Mamatha, Dr. B. Venkatesh, and R. Pramod, “Numerical Integration over Ellipsoid by transforming into 10-noded Tetrahedral Elements”, IOP Conference Series: Materials Science and Engineering, vol. 310, p. 012144, 2018.[Abstract]


In this paper we try to obtain the numerical integration formulas to evaluate volume integrals over an ellipsoid by transforming into a 10-noded standard tetrahedral element. We first transform the ellipsoid to a sphere of radius one. A sphere of radius one in the first octant is divided into six tetrahedral elements (with three straight edges and three curved edges) by choosing a point P on the surface of the sphere. Later we consider each curved tetrahedral element to be 10-noded elements and transform them to standard tetrahedral elements (10-noded) with straight edges. Then we evaluate numerical integral values of some integrands by applying these transformations over the ellipsoid using MATHEMATICA-software. The performance of the proposed method with that of the generated meshes over ellipsoid is analyzed using some example problems. We observe that the ellipsoid has been discretized into 48 standard 10-noded tetrahedral elements and the results are converging to the exact integral values with minimum computational time.

More »»

2015

T. M. Mamatha and Dr. B. Venkatesh, “Gauss quadrature rules for numerical integration over a standard tetrahedral element by decomposing into hexahedral elements”, Applied Mathematics and Computation, vol. 271, pp. 1062-1070, 2015.[Abstract]


In recent years hexahedral elements have gained more importance than compared to tetrahedral elements (e.g. importance in the study of aero-acoustic equations using hexahedral elements to check the computational efficiency between tetrahedral and hexahedral elements). Also among the various integration schemes, Gauss Legendre quadrature which can evaluate exactly the (2n−1)th order polynomial with n-Gaussian points is most commonly used in view of the accuracy and efficiency of calculations. In this paper, we present a Gauss quadrature method for numerical integration over a standard tetrahedral element T[0,1]3 by decomposing into hexahedral elements H[−1,1]3. The method can be used for computing integrals of smooth functions, as well as functions with end-point singularities. The performance of the method is demonstrated with several numerical examples. By the proposed method, with less number of divisions we are obtaining the exact solutions with minimum errors and number of computations is reduced drastically. We have evaluated the aspect ratio value of each hexahedral element which is in the range 1–5, as per the element quality check these elements can be used for mesh generation in FEM.

More »»

2013

H. T. Rathod, Dr. B. Venkatesh, T, S. K., and M, M. T., “Numerical integration over polygonal domains using convex quadrangulation and gauss legendre quadrature rules”, Inernational journal of engineering and computer science, vol. 2, no. 8, pp. 2576–2610, 2013.

2011

Dr. B. Venkatesh, “On Quartic Splines with Applications to Quadrature over Curved Domains”, International e-Journal of Numerical Analysis and Related Topics, vol. 6, pp. 126-146, 2011.

2011

H. T. Rathod, Dr. B. Venkatesh, Nagabhushan, C. S., and Hariprasad, A. S., “On quintic splines with applications to quadrature over curved domains”, International electronic engineering mathematical society, vol. 6, pp. 126–146, 2011.

2011

H. Ta Rathod, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Gauss Legendre - Gauss Jacobi quadrature rules over a Tetrahedral region”, International Journal of Mathematical Analysis, vol. 5, pp. 189-198, 2011.[Abstract]


This paper presents a Gaussian quadrature method for the evaluation of the triple integral I = ∫∫∫/T f (x, y, z) dxdydz, where f (x, y, z) is an analytic function in x, y, z and T refers to the standard tetrahedral region:{(x, y, z) | 0 ≤ x, y, z ≤1, x + y + z ≤1} in three space (x, y, z). Mathematical transformation from (x, y, z) space to (u, v, w) space maps the standard tetrahedron T in (x, y, z) space to a standard 1-cube: {(u,v,w) / 0 ≤ u, v, w ≤1} in (u, v, w) space. Then we use the product of Gauss-Legendre and Gauss-Jacobi weight coefficients and abscissas to arrive at an efficient quadrature rule over the standard tetrahedral region T. We have then demonstrated the application of the derived quadrature rules by considering the evaluation of some typical triple integrals over the region T.

More »»

2010

Dr. B. Venkatesh, “The use of quintic splines for high accuracy function and integral function approximations”, International Electronic Engineering Mathematical Society, vol. 4, pp. 104-128, 2010.

2010

Dr. B. Venkatesh, “On quartic splines with applications to function and integral function approximations”, International Electronic Engineering Mathematical Society, vol. 4, pp. 73-103, 2010.

2010

H. T. Rathod, Hariprasad, A. S., Dr. B. Venkatesh, and Nagabhushan, C. S., “The use of quintic splines for high accracy function and integrable function approximations”, International electronic engineering mathematical society, vol. 4, pp. 104–128, 2010.

2010

H. T. Rathod, Nagabhushan, C. S., Dr. B. Venkatesh, and , “On quintic splines with applications to function and integrable function approximations”, International electronic engineering mathematical society, vol. 4, pp. 73–103, 2010.

2008

H. T. Rathod, Nagaraja, K. V., Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “The use of parabolic arcs in matching curved boundaries by point transformations for some higher order triangular elements”, Finite Elements in Analysis and Design, vol. 44, pp. 920-932, 2008.[Abstract]


This paper is concerned with curved boundary triangular elements having one curved side and two straight sides. The curved elements considered here are the 6-node (quadratic), 10-node (cubic), 15-node (quartic) and 21-node (quintic) triangular elements. On using the isoparametric coordinate transformation, these curved triangles in the global (x,y) coordinate system are mapped into a standard triangle: (ξ,η)/0⩽ξ,η⩽1,ξ+η⩽1 in the local coordinate system (ξ,η). Under this transformation curved boundary of these triangular elements is implicitly replaced by quadratic, cubic, quartic and quintic arcs. The equations of these arcs involve parameters, which are the coordinates of points on the curved side. This paper deduces relations for choosing the parameters in quartic and quintic arcs in such a way that each arc is always a parabola which passes through four points of the original curve, thus ensuring a good approximation. The point transformations which are thus determined with the above choice of parameters on the curved boundary and also in turn the other parameters in the interior of curved triangles will serve as a powerful subparametric coordinate transformation for higher order curved triangular elements with one curved side and two straight sides.

More »»

2007

H. T. Rathod, Dr. B. Venkatesh, Nagaraja, K. V., and Islam, M. Shafiqul, “Gauss Legendre–Gauss Jacobi quadrature rules over a tetrahedral region”, Applied Mathematics and Computation, vol. 190, pp. 186-194, 2007.[Abstract]


This paper presents a Gaussian Quadrature method for the evaluation of the triple integral ∫∫T∫f(x,y,z)dxdydz, where f(x,y,z) is an analytic function in x, y, z and T refers to the standard tetrahedral region: (x,y,z)0⩽x,y,z⩽1,x+y+z⩽1 in three space (x,y,z). Mathematical transformation from (x,y,z) space to (U,V,W) space map the standard tetrahedron T in (x,y,z) space to a standard 1-cube: (U,V,W)/0⩽U,V,W⩽1 in (U,V,W) space. Then we use the product of Gauss Legendre and Gauss Jacobi weight coefficients and abscissas to arrive at an efficient quadrature rule over the standard tetrahedral region T. We have then demonstrated the application of the derived quadrature rules by considering the evaluation of some typical triple integrals over the region T.

More »»

2007

H. T. Rathod, Dr. B. Venkatesh, and Nagaraja K V, “Symmetric Gauss Legendre quadrature formulas for composite numerical integration over a triangular surface”, Applied Mathematics and Computation, vol. 188, no. 1, pp. 865–876, 2007.[Abstract]


This paper first presents a Gauss Legendre quadrature method for numerical integration of View the MathML source, where f(x, y) is an analytic function in x, y and T is the standard triangular surface: {(x, y)∣0 ⩽ x, y ⩽ 1, x + y ⩽ 1} in the Cartesian two dimensional (x, y) space. We then use a transformation x = x(ξ, η), y = y(ξ, η ) to change the integral I to an equivalent integral View the MathML source, where S is now the 2-square in (ξ, η) space: {(ξ, η)∣ − 1 ⩽ ξ, η ⩽ 1}. We then apply the one dimensional Gauss Legendre quadrature rules in ξ and η variables to arrive at an efficient quadrature rule with new weight coefficients and new sampling points. We then propose the discretisation of the standard triangular surface T into n2 right isosceles triangular surfaces Ti (i = 1(1)n2) each of which has an area equal to 1/(2n2) units. We have again shown that the use of affine transformation over each Ti and the use of linearity property of integrals lead to the result:
where View the MathML source and x = xi(X, Y) and y = yi(X, Y) refer to affine transformations which map each Ti in (x, y) space into a standard triangular surface T in (X, Y) space. We can now apply Gauss Legendre quadrature formulas which are derived earlier for I to evaluate the integral View the MathML source. We observe that the above procedure which clearly amounts to Composite Numerical Integration over T and it converges to the exact value of the integral View the MathML source, for sufficiently large value of n, even for the lower order Gauss Legendre quadrature rules. We have demonstrated this aspect by applying the above explained Composite Numerical Integration method to some typical integrals.

More »»

2007

H. T. Rathod, Dr. B. Venkatesh, and Nagaraja, K. V., “On the application of two Gauss–Legendre quadrature rules for composite numerical integration over a tetrahedral region”, Applied mathematics and computation, vol. 189, pp. 131–162, 2007.[Abstract]


In this paper we first present a Gauss–Legendre quadrature rule for the evaluation of View the MathML source, where f(x, y, z) is an analytic function in x, y, z and T is the standard tetrahedral region: {(x, y, z)∣0 ⩽ x, y, z ⩽ 1, x + y + z ⩽ 1} in three space (x, y, z). We then use a transformation x = x(ξ, η, ζ), y = y(ξ, η, ζ) and z = z(ξ, η, ζ ) to change the integral into an equivalent integral View the MathML source over the standard 2-cube in (ξ, η, ζ) space: {(ξ, η, ζ)∣ −1 ⩽ ξ, η, ζ ⩽ 1}. We then apply the one-dimensional Gauss–Legendre quadrature rules in ξ, η and ζ variables to arrive at an efficient quadrature rule with new weight coefficients and new sampling points. Then a second Gauss–Legendre quadrature rule of composite type is obtained. This rule is derived by discretising the tetrahedral region T into four new tetrahedra View the MathML source (i = 1, 2, 3, 4) of equal size which are obtained by joining the centroid of T, c = (1/4, 1/4, 1/4) to the four vertices of T . By use of the affine transformations defined over each View the MathML source and the linearity property of integrals leads to the result: More »»

2007

H. T. Rathod, Nagaraja, K. V., and Dr. B. Venkatesh, “Numerical integration of some functions over an arbitrary linear tetrahedra in Euclidean three-dimensional space”, Applied Mathematics and Computation, vol. 191, pp. 397-409, 2007.[Abstract]


In this paper it is proposed to compute the volume integral of certain functions whose antiderivates with respect to one of the variates (say either x or y or z) is available. Then by use of the well known Gauss Divergence theorem, it can be shown that the volume integral of such a function is expressible as sum of four integrals over the unit triangle. The present method can also evaluate the triple integrals of trivariate polynomials over an arbitrary tetrahedron as a special case. It is also demonstrated that certain integrals which are nonpolynomial functions of trivariates x,y,z can be computed by the proposed method. We have applied Gauss Legendre Quadrature rules which were recently derived by Rathod et al. [H.T. Rathod, K.V. Nagaraja, B. Venkatesudu, N.L. Ramesh, Gauss Legendre Quadrature over a Triangle, J. Indian Inst. Sci. 84 (2004) 183–188] to evaluate the typical integrals governed by the proposed method.

More »»

2007

H. T. Rathod, Nagaraja, K. V., and Dr. B. Venkatesh, “On the application of two symmetric Gauss Legendre quadrature rules for composite numerical integration over a triangular surface”, Applied mathematics and computation, vol. 190, pp. 21–39, 2007.[Abstract]


This paper first presents a Gauss Legendre quadrature rule for the evaluation of View the MathML source, where f(x,y) is an analytic function in x, y and T is the standard triangular surface: {(x,y)|0⩽x,y⩽1,x+y⩽1} in the two space (x,y). We transform this integral into an equivalent integral View the MathML source where S is the 2-square in (ξ, η ) space: {(ξ,η)|-1⩽ξ,η⩽1}. We then apply the one-dimensional Gauss Legendre quadrature rules in ξ and η variables to arrive at an efficient Quadrature rules with new weight coefficients and new sampling points. Then a second Gauss Legendre quadrature rule of composite type is obtained. This rule is derived by discretising T into three new triangles View the MathML source of equal size which are obtained by joining centroid of T , C=(1/3,1/3) to the three vertices of T . By use of affine transformations defined over each View the MathML source and the linearity property of integrals leads to the result:

More »»

2006

H. T. Rathod, Dr. B. Venkatesh, and Nagaraja, K. V., “On the application of two symmetric Gauss Legendre quadrature rules for composite numerical integration over a tetrahedral region”, International Journal for Computational Methods in Engineering Science and Mechanics, vol. 7, no. 6, pp. 445–459, 2006.[Abstract]


In this paper, we first present a Gauss Legendre Quadrature rule for the evaluation of I = ∫∫∫T f(x,y,z) dxdydz , where f(x,y,z) is an analytic function in x,y,z and T is the standard tetrahedral region: {(x,y,z) |0 ≤ x,y,z ≤ 1,x + y + z ≤ 1} in three space ( x,y,z) . We then use the transformations x = x(ξ,η,ζ), y = y (ξ,η,ζ) and z = z(ξ,η,ζ) to change the integral I into an equivalent integral I = ∫− 1 1∫− 1 1∫− 1 1f(x(ξ,η,ζ),y(ξ,η,ζ),z(ξ,η,ζ)) dξ dη dζ over the standard 2-cube in (ξ,η,ζ) space: {(ξ,η,ζ) | − 1 ≤ ξ,η,ζ ≤ 1} . We then apply the one-dimensional Gauss Legendre Quadrature rule in ξ , η and ζ variables to arrive at an efficient quadrature rule with new weight coefficients and new sampling points. Then a second Gauss Legendre Quadrature rule of composite type is obtained. This rule is derived by discretising the tetrahedral region T into four new tetrahedra Ti c ( i = 1,2,3,4) of equal size, which are obtained by joining centroid of T, c = (1/4, 1/4, 1/4) to the four vertices of T. Use of the affine transformations defined over each Ti c and the linearity property of integrals leads to the result:

More »»

2006

H. T. Rathod, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Gauss legendre quadrature formulas over a tetrahedron”, Numerical Methods for Partial Differential Equations, vol. 22, pp. 197–219, 2006.[Abstract]


In this article we consider the Gauss Legendre Quadrature method for numerical integration over the standard tetrahedron: {(x, y, z)|0 ≤ x, y, z ≤ 1, x + y + z ≤ 1} in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: {(ξ, η, ζ)| − 1 ≤ ζ, η, ζ ≤ 1} in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points. The effectiveness of the formulas is demonstrated by applying them to the integration of three nonpolynomial, three polynomial functions and to the evaluation of integrals for element stiffness matrices in linear three-dimensional elasticity. © 2005 Wiley Periodicals, Inc. Numer Methods Partial Differential Eq, 2006

More »»

2005

H. T. Rathod, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Gauss Legendre Quadrature Formulae for Tetrahedra”, International Journal for Computational Methods in Engineering Science and Mechanics, vol. 6, pp. 179-186, 2005.[Abstract]


In this paper we consider the Gauss Legendre quadrature method for numerical integration over the standard tetrahedron: (x, y, z)| 0 ≤ x, y, z ≤ 1, x + y + z ≤ 1 in the Cartesian three-dimensional (x, y, z) space. The mathematical transformation from the (x, y, z) space to (ξ, η, ζ) space is described to map the standard tetrahedron in (x, y, z) space to a standard 2-cube: (ξ, η, ζ)| − 1 ≤ ξ, η, ζ ≤ 1 in the (ξ, η, ζ) space. This overcomes the difficulties associated with the derivation of new weight co-efficients and sampling points. The effectiveness of the formulae is demonstrated by applying them to the integration of three nonpolynomial and three polynomial functions.

More »»

2005

H. T. Rathod, Dr. B. Venkatesh, and Dr. K.V. Nagaraja, “Symmetric Gauss Legendre quadrature rules for composite numerical integration over a tetrahedral region”, Journal of Bulletin of Mathematics, vol. 24, pp. 51–79, 2005.

2004

Dr. B. Venkatesh, “Gauss Legendre quadrature over a triangle Journal of Mathematics & Information Technology”, Acharya Nagarjuna International Journal of Mathematics & Information Technology, vol. 1, no. 1, pp. 33-52, 2004.

2004

H. Ta Rathod, Dr. K.V. Nagaraja, Dr. B. Venkatesh, and Ramesh, N. Ld, “Gauss Legendre quadrature over a triangle”, Journal of the Indian Institute of Science, vol. 84, pp. 183-188, 2004.[Abstract]


This paper presents a Gauss Legendre quadrature method for numerical integration over the standard triangular surface: {(x, y) | 0 ≤ x, y ≤ 1, x + y ≤ 1} in the Cartesian two-dimensional (x, y) space. Mathematical transformation from (x, y) space to (ξ, η) space map the standard triangle in (x, y) space to a standard 2-square in (ξ, η) space: {(ξ, η)|-l ≤ ξ, η ≤ 1}. This overcomes the difficulties associated with the derivation of new weight coefficients and sampling points and yields results which are accurate and reliable. Results obtained with new formulae are compared with the existing formulae.

More »»

Publication Type: Conference Paper

Year of Publication Title

2019

Dr. K. Murali, Dr. V. Kesavulu Naidu, and Dr. B. Venkatesh, “Solution of Darcy-Brinkman-Forchheimer Equation for Irregular Flow Channel by Finite Elements Approach”, in Journal of Physics: Conference Series, 2019, vol. 1172.[Abstract]


The finite element method of solution with curved triangles to solve the three-dimensional, fully-developed Darcy-Brinkman-Forchheimer flow equation in channel with curved side is solved using quasi-linearization and Gauss-Seidel iteration method. Exhaustive numerical computation and numerical experimentation reveals the parameters' influence on the velocity distributions. A salient feature of the method adopted in the present paper is that it ensures that the errors are almost equally distributed among all the nodes. It is found that the irregular cross-section channel with upward concave boundary decelerates the flow. Numerical experimentation involved different order curved triangular elements and extensive computation revealed that the quintic order curved triangular element yields the desired solution to an accuracy of 10 -5 . The finite element method is found to be very effective in capturing boundary and inertia effects in the three-dimensional, fully-developed flow through porous media. Further, it prevails with regards to giving the required answer for vast estimations of Forchheimer number when shooting technique fails to do as such. The technique can be effortlessly utilized in some other sporadic cross-area channel. © Published under licence by IOP Publishing Ltd.

More »»
Faculty Research Interest: