The Finite Volume Method (FVM) is a numerical technique in which the integral formulation of theconservation laws is discretized directly in the physical space.It is the most widely used method today in CFD. The advantages of nite volume method are its easeof implementation on arbitrary grids and complex geometry.The FVM has the great advantage that the conservative discretization is automatically satised.Its implementation is directly related to the physics of the problem.The FVM consists of the following steps:ˆ Subdivide the computational domain into non-overlapping control volumes also known as nite volumes.ˆ Apply the integral conservation law to each of these nite volumes Conservation law∂∂t ˆΩU dΩ + ˛SF~·dS~ =ˆΩQApplying Conservation law to individual volumes∂∂t ˆΩ1U dΩ + ˛ABCAF~·dS~ =ˆΩ1Q∂∂t ˆΩ2U dΩ + ˛DEBDF~·dS~ =ˆΩ2Q∂∂t ˆΩ3U dΩ + ˛AEDAF~·dS~ =ˆΩ3Q4(a) Cell Centered Control volume (b) Vertex Centered Control VolumeFigure 3: Types of control volumesControl volume denitionThere are two types of Finite volume method based on control volume denition.a) Cell-centered Finite volume , where the unknowns are stored/located at the centers of the mesh cellsand the grid lines dene the nite volumes and surfaces.b) Cell- Vertex Finite volume - also known as the vertex centered nite volume, here the unknownvariables are stored at the vertex/nodes of the mesh. A control volume is dened around this node.There are dierent varieties of control volume denitions possible for this type of schem

explain finite volume method: 'Conservation law∂∂t ˆΩU dΩ + ˛SF~·dS~ =ˆΩQApplying Conservation law to individual volumes∂∂t ˆΩ1U dΩ + ˛ABCAF~·dS~ =ˆΩ1Q∂∂t ˆΩ2U dΩ + ˛DEBDF~·dS~ =ˆΩ2Q∂∂t ˆΩ3U dΩ + ˛AEDAF~·dS~ =ˆΩ3Q4(a) Cell Centered Control volume (b) Vertex Centered Control VolumeFigure 3: Types of control volumesControl volume denitionThere are two types of Finite volume method based on control volume denition.a) Cell-centered Finite volume , where the unknowns are stored/located at the centers of the mesh cellsand the grid lines dene the nite volumes and surfaces.b) Cell- Vertex Finite volume - also known as the vertex centered nite volume, here the unknownvariables are stored at the vertex/nodes of the mesh. A control volume is dened around this node.There are dierent varieties of control volume denitions possible for this type of scheme'

explain explicite finite difference method/approach in CFD

Explain in details difference between Finite Element Method and Finite Difference Method. technicaly answer engineering level

The shooting method is used forQuestion 13Answera.solving Initial value problems (IVPs)b.solving boundary value problems (BVPs)c.solving PDEs

Von Neumann stability analysis tells us:Group of answer choicesThat all numerical schemes based on finite differences are stableThe conditions for stability of a numerical scheme based on finite differencesThat all numerical schemes based on finite differences are unstableThat the amplitude of modes in a Fourier series solution always increases