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The most commonly used coordinate system on the sphere is the geographic system ( λ , φ ) . The curvilinear nature of these coordinates on the sphere lead to some “metric” terms in the component momentum equations. Under the thin-atmosphere and hydrostatic approximations these terms are discretized:

(2.101) A w Δ r f h w G m e t r i c u = ¯ ¯ u i a tan φ A c Δ r f h c ¯ v j i
(2.102) A s Δ r f h s G m e t r i c v = ¯ ¯ u i a tan φ A c Δ r f h c ¯ u i j
(2.103) G m e t r i c w = 0

where a is the radius of the planet (sphericity is assumed) or the radial distance of the particle (i.e. a function of height). It is easy to see that this discretization satisfies all the properties of the discrete Coriolis terms since the metric factor u a tan φ can be viewed as a modification of the vertical Coriolis parameter: f f + u a tan φ .

The DST3 method described above must be used in a forward-in-time manner and is stable for 0 | c | 1 . Although the scheme appears to be forward-in-time, it is in fact third order in time and the accuracy increases with the Courant number! For low Courant number, DST3 produces very similar results (indistinguishable in Figure 2.10 ) to the linear third order method but for large Courant number, where the linear upwind third order method is unstable, the scheme is extremely accurate ( Patrizia Pepe Handbags Dark Blue zoGv5
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The overshoots in the DST3 method can be controlled with a flux limiter. The limited flux is written:

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F = 1 2 ( u + | u | ) ( τ i 1 + ψ ( r + ) ( τ i τ i 1 ) ) + 1 2 ( u | u | ) ( τ i 1 + ψ ( r ) ( τ i τ i 1 ) )
r + = τ i 1 τ i 2 τ i τ i 1 r = τ i + 1 τ i τ i τ i 1

and the limiter is the Sweby limiter:

The breast augmentation procedure lasts one to two hours and is typically performed with general anesthesia. Incisions are made in inconspicuous places on the breast to minimize scar visibility. These may be located:

The breast is then lifted, creating a pocket into which the implant is inserted.

Saline implants may also be placed endoscopically through an incision in the navel. This minimally invasive breast enhancement technique is known as a transumbilical breast augmentation or TUBA approach.

Implant placement beneath the muscle of the chest offers a few advantages over placement beneath the breast tissue only. These include reduced risk of capsular contracture (post-operative tightening around the implant) and less interference with mammogram examinations. Possible disadvantages include need for drainage tubes and elevated pain in the first few days following surgery. We will discuss which option may be best for you.

In the TUBA procedure, implants cannot be placed beneath the chest wall.

After the implants have been inserted and positioned beneath the nipples, the incisions are stitched closed, then taped and bandaged. In a few days, these bandages may be replaced with a surgical bra.

Most patients feel tired and sore after breast augmentation surgery, but this usually passes in a day or two. Many patients return to work within the week.

Stitches are removed in a week to 10 days after breast augmentation. Any post-operative pain, swelling and sensitivity will diminish over the first few weeks.

Scars from breast augmentation incisions will begin to fade in a few months and will continue to fade for months or years.

Complications following breast augmentation surgery are uncommon and usually minimal. They may include capsular contracture, swelling and pain, infection around the implant, a change in nipple sensation, milk production if you nursed a baby within a year before the procedure, and breakage or leakage of the implant (implant rupture) as a result of injury or the normal compression and movement of your breast.

If a saline implant ruptures, the implant will simply deflate in a few hours and your body will absorb the salt water. If a silicone implant leaks, you will need to see a doctor immediately. Regular monitoring of breast implants after breast augmentation is recommended to ensure continuing breast and implant health.

Contact us today to schedule a breast augmentation consultation!

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