A CONTROL VOLUME-BASED FINITE-ELEMENT METHOD FOR SOLVING THE NAVIER-STOKES EQUATIONS USING EQUAL-ORDER VELOCITY-PRESSURE INTERPOLATION

A control volume-based finite-element method for solving the Navier-Stokes equations using equal-order velocity-pressure interpolation is presented. Unlike the unequal-order-type methods that compute pressure at much fewer grid points than velocity, the proposed equal-order method calculates velocity and pressure at all the grid points in the domain. The validity of the method is established by applying it to solve some test problems

[1]  Robert L. Lee,et al.  The cause and cure (!) of the spurious pressures generated by certain fem solutions of the incompressible Navier‐Stokes equations: Part 2 , 1981 .

[2]  T. Chung,et al.  Finite Element Analysis in Fluid Dynamics , 1978 .

[3]  R. T. Cheng,et al.  Numerical Solution of the Navier‐Stokes Equations by the Finite Element Method , 1972 .

[4]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[5]  H. Schlichting.  Boundary Layer Theory , 1955 .

[6]  P. Hood,et al.  A numerical solution of the Navier-Stokes equations using the finite element technique , 1973 .

[7]  B. R. Baliga,et al.  A CONTROL VOLUME FINITE-ELEMENT METHOD FOR TWO-DIMENSIONAL FLUID FLOW AND HEAT TRANSFER , 1983 .

[8]  O. C. Zienkiewicz,et al.  An ‘upwind’ finite element scheme for two‐dimensional convective transport equation , 1977 .

[9]  Graham F. Carey,et al.  Variable upwinding and adaptive mesh refinement in convection‐diffusion , 1983 .

[10]  B. R. Baliga,et al.  SOLUTION OF SOME TWO-DIMENSIONAL INCOMPRESSIBLE FLUID FLOW AND HEAT TRANSFER PROBLEMS, USING A CONTROL VOLUME FINITE-ELEMENT METHOD , 1983 .

[11]  R. S. Marshall,et al.  Viscous incompressible flow by a penalty function finite element method , 1981 .

[12]  B. R. Baliga.  A control-volume based finite element method for convective heat and mass transfer , 1978 .

[13]  M. Yovanovich,et al.  Finite-element solution procedures for solving the incompressible, Navier-Stokes equations using equal order variable interpolation , 1978 .

[14]  Robert L. Lee,et al.  A comparison of various mixed-interpolation finite elements in the velocity-pressure formulation of the Navier-Stokes equations☆ , 1978 .

[15]  J. Tinsley Oden,et al.  Analysis of Flow of Viscous Fluids by the Finite-Element Method , 1972 .

[16]  B. R. Baliga,et al.  A NEW FINITE-ELEMENT FORMULATION FOR CONVECTION-DIFFUSION PROBLEMS , 1980 .

[17]  E. Becker,et al.  Finite element analysis of viscous, incompressible fluid flow , 1976 .