Singularity methods in fluid dynamics
Abstract
Flow fields are governed by differential equations for certain variables such as velocity potential, pressure, and temperature. In many cases these equations are linear and then socalled fundamental solutions play an important role. These are solutions of the homogeneous equations except at a single point where the solution has a singularity. For boundary value problems of homogeneous linear differential equations the solution can be built up from fundamental solutions with their singularities situated at the boundary of the field. The problem is then reduced to the determination of the strength of these singularities. Usually the boundary condition leads to an integral equation for the unknown strength. If the equation is nonhomogeneous, the known right hand side gives rise to a solution containing an integration over a distribution of singularities of known strength in the whole field. In order to satisfy the boundary conditions singularities of unknown strength at the boundary must also be added in this case.
 Publication:

In Von Karman Inst. for Fluid Dyn. Math. Methods in Fluid Mech. 41 p (SEE N8115288 0634
 Pub Date:
 1980
 Bibcode:
 1980mmfm.vkif.....V
 Keywords:

 Boundary Value Problems;
 Differential Equations;
 Flow Distribution;
 Fluid Mechanics;
 Linear Equations;
 Problem Solving;
 Singularity (Mathematics);
 Boundary Conditions;
 Homogeneity;
 Integral Equations;
 Numerical Analysis;
 Fluid Mechanics and Heat Transfer