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Absorbing Boundary Conditions ( ABCs) (2 Sessions ) (1 Task)

Absorbing Boundary Conditions ( ABCs) (2 Sessions ) (1 Task)

Absorbing Boundary Conditions ( ABCs) (2 Sessions ) (1 Task). Absorbing Boundary Conditions (ABC). First-order ABCs are those which estimate value of fields outside boundary by looking back one step in time and one grid cell in space.

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977 views • 30 slides
Introduction to Computational Fluid Dynamics Lecture 1: Review

Introduction to Computational Fluid Dynamics Lecture 1: Review

Introduction to Computational Fluid Dynamics Lecture 1: Review. Introductions. Instructor Bio Ph.D in ME (CFD applications in Materials Processing) Post Doctoral Fellowship at Stanford (Hydrodynamic instabilities in cavity flows) 7 years of cfd development at FDI, Fluent

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1.41k views • 27 slides
Exact Equations

Exact Equations

Exact Equations. Nonlinear Non-separable First Order Equations. Techniques We Know. Nonlinear Separable. Separation of Variables. Integrating Factors. Linear. Non-separable. Nonlinear. Implicit Differentiation. Note:. Implicit Differentiation. Implicit Differentiation.

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944 views • 26 slides
Warm-Up

Warm-Up

Warm-Up. Write the following polynomial in its factored form and then sketch it: Double root at (-5,0), triple root at (-3,0), single root at (0,0) and a triple root at (4,0). The leading term is positive. Expand the following terms:. Exact Graphs of Polynomials. Learning Targets.

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400 views • 24 slides
(1) The order of ODE: the order of the highest derivative e.g.,

(1) The order of ODE: the order of the highest derivative e.g.,

Chapter 14 First-order ordinary differential equation. (1) The order of ODE: the order of the highest derivative e.g.,. (2) The degree of ODE: After the equation has been rationalized, the power of the highest-order derivative. e.g.,.

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634 views • 20 slides
Ch 2.6: Exact Equations & Integrating Factors

Ch 2.6: Exact Equations & Integrating Factors

Ch 2.6: Exact Equations & Integrating Factors. Consider a first order ODE of the form Suppose there is a function ? such that and such that ? ( x,y ) = c defines y = ? ( x ) implicitly. Then and hence the original ODE becomes Thus ? ( x,y ) = c defines a solution implicitly.

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1.21k views • 10 slides
Warm-up Problems

Warm-up Problems

Warm-up Problems. Solve the IVP . Give the largest interval over which the solution is defined. Exact Equations. Recall that we defined the differential of z = f ( x , y ) as dz = f x dx + f y dy

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172 views • 9 slides

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